# An analysis of structural change in the telecommunications industry.

An Analysis of Structural Change in the Telecommunications Industry

Introduction

Enormous changes have occured in the telecommunications industry over the past decade. Obviously, one of the biggest events was the breakup of the Bell System which occured in January 1984. But a number of other changes have also taken place. The emergence of alternative providers and the wholesale introduction of new services have given customers increased choices and flexibility to meet their long distance needs. In addition, technological advancements resulting in such services as integrated services digital network (ISDN) promises to open up new opportunities in long distance provisioning. Moreover, as the structure of the U.S. economy changes, so does the use of telecommunications in the industrial process. Data transmission and the ability of computers to communicate over long distance networks have become increasingly important. As business needs have changed, long distance no longer means simply making a telephone call.

Therefore, from both the buying side and the selling side, it can be seen that the industry is changing. Given this, a natural avenue of inquiry might be to ask if statistical evidence of these changes can be found. In other words, does an analysis of the data indicate that such shifts are occurring and what is the nature of these shifts? Knowledge of this would validate the view that the telecommunications industry is undergoing the large scale transformation that has long been predicted. This information would also be useful from an analytical perspective when studying the various types of statistical and economic relationships that are found in telecommunications. Changes in the nature of these relationships would require that this new information be taken into account when generating forecasts or analyzing various issues that affect the telecommunications industry.

Methodology and Data

A strictly time-series approach was utilized here. That is, no economic or price data were used. The intent was to focus solely on the data series itself and to also take advantage of some recent advances in the analysis of time-series data. The series that was analyzed consisted of quarterly interstate volumes for the entire telecommunications industry. This included all interstate services across all long distance carriers. The series was then converted to total holding time in hundred call seconds (THTCCS). THTCCS is an internal AT&T measure of network utilization which includes such characteristics as call set-up time. For a number of applications, it is considered the most relevant measure of the demand that is placed on a network. The data series ran from 1976:1 through 1987:3.(1)

Since the purpose of this paper was to focus on structural changes in the telecommunications industry, a natural place to start was with divestiture which began on January 1, 1984. Therefore, we first considered a sample running from 1976 through 1983. Given this, the next step was to derive the model specification that best represented the series over that interval. In initial estimations, convergence problems often occurred when including moving-average components in the equation. Consequently, moving-average terms were eliminated from subsequent regressions. When the series was measured in levels, an examination of its autocorrelations suggested that the data was nonstationary. Consistent with this was that the estimation of simple ARIMA models indicated the possibility of unit roots. We then formally tested for the presence of unit roots. In other words, in the simple formulation, (1) Y sub t = a + bY sub t-1 + e sub t we wanted to test the null that b = 1. In this case, conventional asymptotic distribution theory could not be applied. Dickey develops an alternate distribution for b. Under the null hypothesis, it has "tau-distribution" that is not the standard t-distribution. The distribution of the tau-statistic was generated using a computer simulation developed by Fuller [9]. An alternative way of expressing the above formulation can be seen by subtracting Y(t-1) from both side giving us the expression, (2) Delta Y sub t = a + (b-1)Y sub t-1 +e sub t.

In other words, a test for the presence of a unit root requires regressing first differences on the lagged level value of the dependent variable and testing for its significance. Lagged first-differenced variables can also be included and tested for significance. Dickey and Fuller [7] show that (b-1) has a tau-distribution. This makes testing for a unit root straightforward in that we can use the ratio of the coefficient and standard error for the lagged level term and compare this statistic with the distribution table prepared by Fuller.

In this case, (b-1)=-.007 with a standard error of .017. Therefore, the tau-statistic was -.007/.017 = -.41. Comparing this to a critical value of -2.93 at the five percent level of significance, we found that this was not significant and we did not reject the null that b = 1. Therefore, modeling in first differences was an appropriate course of action. A similarly constructed test rejected the use of second differences. Given that we could not reject the hypothesis of first differences, we then systematically tested for the optimal lag length using standard t-tests. The t-statistics for lags three through six were less than one and therefore rejected. The final accepted result was: (3) Delta Y sub t = .237 - .413 Delta Y sub t-1 - .387 Delta Y sub t-2 (.016)(.172) (.173) Q(12)=10.3 AIC=-18.6 SBC=-14.3 R raised to 2=.28

The numbers in parenthesis represent standard errors. The t-statistics indicated that the coefficients were different from zero. A Box-Pierce Q-Test for 12 autocorrelations generated a Q-statistic equal to 10.3 which with nine degrees of freedom was less than the critical value of 21.03 at the five percent level of significance indicating that the residuals were white noise. In addition, the Akaike Information Criterion (AIC) and the Schwartz Bayesian Criterion (SBC) were provided as measures of goodness-of-fit used to compare non-nested alternative model specifications. Of the models tested, this form minimized the SBC while the AIC was the second smallest. Although an ARIMA (3,1,3) minimized the AIC, the ARIMA (2,1,0) specification was clearly superior in terms of the overall diagnostics. The R2=.28 indicated a fairly good fit in first differences.2 In addition, there was little indication of seasonality. The model was estimated using a maximum likelihood method. The results differed little when least-squares methods were employed. Therefore, we found that this formulation was a reasonable representation of the data series relative to other models.3

Structural Change

The possibility of a structural change in the series was then considered. Following Chow [6] and using the ARIMA (2,1,0) functional form, an additional four observations (the year 1984) were added to the sample. In this case, F-tests at the one percent and five percent levels of significance did not lead to a rejection of the null hypothesis of no structural change. The inclusion of four more observations for 1985 also did not change these results. For the sake of comparison, the regression results for the 1976-1985 sample were: (4) Delta Y sub t = .255 - .346 Delta Y sub t-1 - .331 Delta Y sub t-2 (.016)(.156) (.158) Q(12)=11.6 AIC=-23.5 SBC=-18.5 R raised to 2=.179

As can be seen, the coefficients changed relatively little while the fit remained reasonably good. In estimating this sample, we found that this specification minimized the SBC although an ARIMA (3,1,0) model minimized the AIC.

However, when the observations for 1986 were added, the Chow test indicated the likelihood of a structural change in the series. The values of the coefficients dropped and the overall fit deteriorated. And when data through 1987 were used, we saw even larger changes in the coefficients and the model fit. Using the entire 1976-1987 sample and an ARIMA (2,1,0) form resulted in: (5) Delta Y sub t = .311 - .031 Delta Y sub t-1 + .231 Y sub t-2 (.042)(.159) (.160) Q(12)=26.8 AIC=-1.37 SBC=4.1 R raised to 2=.051

As can be seen, the signs and values of the coefficients changed considerably and both lags became insignificant. With an R2 = .051, the fit of this specification deteriorated to the point where it was only marginally better than a random walk model. And with a critical value of 16.9 at the five percent level and 21.7 at the one percent level, we also concluded that the residuals were no longer white noise. A further examination of the series when measured in first differences indicated that its variance increased beginning in 1986.

Therefore, standard tests indicated that from a time-series perspective, the statistical relationship between total long distance telecommunications demand and its lagged values had undergone significant changes. Although divestiture occurred in 1984, the evidence suggests that these aggregate relationships significantly shifted beginning in 1986.

Structural Change and the

Presence of Outliers

In order to more closely examine the type of structural change that the initial regression results suggested, a number of further tests were performed on the data. The tests involved the detection of outlier observations. The basic approach follows the framework developed by Tsay [14] and was modified somewhat for this analysis. Outliers in this case represent anomalous observations not consistent with the whole of the data series. There are more formal definitions, but one simple approach classifies outliers in terms of the number of standard deviations an observation may be from the mean or moving-average. Outliers may take several forms. They could represent a one-time "shock" to the data which occurs because of reporting problems or a one-time event, the impact of which is completed in one period. They can also be a level change in the data which could be the result of a permanent structural shift or perhaps a transitory shock whose impact decays as time increases.

Briefly, there are several steps to the creation of these outlier detection tests. The basic framework was developed by Box and Tiao [2] and further extended by Chang [3], Chang and Tiao [4], Chen and Tiao [5] and Tsay [13]. This method requires the transformation of the data series using the values of the series as well as weights that are based on an initial ARIMA model estimation. These transformed variables are employed in a subsequent regression, the coefficients and standard errors of which are used to create a series of ratio tests that are sequentially applied to every observation in the sample. The null hypothesis is that a particular observation is not an outlier while the various alternative hypotheses consist of the different types of outliers. Under the null, this statistic has a N(0,1) distribution. For more information regarding these tests, see the citations above.

In our approach, since tests for structural change indicated that there were no significant shifts among the coefficients through the end of 1985, this specification and its coefficient estimates were then imposed on the entire series and the individual observations were then systematically tested for the presence of outliers.4 The results of the tests were interesting.5 Outlier observations were detected at three places. The first two represented additive or one-time displacements at 1979:3 and at 1982:1 where total network demand was significantly lower than in adjacent periods. The likely explanation for the drop in 1982:1 was the severe recession with the 1981:4 real GNP declining at a five percent annual rate and 1982:1 showing a six percent annual decline. Economics alone would not seem to be the explanation for the 1979 outlier. There are several other possible explanations including recording problems.

The third represents a series of outliers that were detected beginning in 1986 and continued through the end of the sample. Here, the outlier uncovered was of a permanent nature that indicated that a structural change had occurred in the series. The actual values of the series were significantly higher than the data up to that point would suggest would be reasonable. Unlike the 1982:1 outlier, economic factors do not seem to play a dominant role in explaining the observations seen here. Economic growth rates were modest during this period compared to interstate long distance growth.

By way of an extension of this analysis, when the regressions that were estimated using samples taken from 1976-1983, 1976-1984, and 1976-1986 were tested, outliers were detected at the same locations as those found when using the 1976-1985 sample.

As a result of the tests that were performed on the data, it appears that structural shifts occurred in the values of THTCCS beginning in 1986 with one-time changes occurring in 1979 and 1982.(6) According to the statistical analysis of them, the 1986 values represent permanent shifts in the series.

Another Approach to Outlier Detection

In an attempt to test the above results, a second method was also tried. The methodology that was initially used to derive a suitable model over the 1976-1983 sample was applied to the entire sample. Again, unit root tests indicated that first differences were appropriate. In this case, a random walk model and an ARIMA (4,1,0) model were selected as among the best forms for this series. Although the random walk minimized the SBC, the ARIMA (4,1,0) minimized the AIC. The ARIMA (4,1,0) was finally selected because its goodness-of-fit was superior to the random walk. The complete results for this model were: (6) Delta Y sub t = .36 - .16 Delta Y sub t-1 + .22 Delta Y sub t-2 + .47 Y sub t-3 + .24 Delta Y sub t-4 (.13)(.15) (.14) (.16) (.18) Q(12)=12.2 AIC=-7.4 SBC=1.8 R raised to 2=.245

Given this model, the outlier detection mechanism was applied. There was evidence of an additive outlier in 1979:3 and then a permanent shift beginning in 1986:3. The 1982:1 additive outlier was not detected. In addition, the permanent outliers were not flagged until 1986:3. Consequently, the overall conclusions are roughly the same in terms of the location of the outlier observations, although the use of the 1976-1987 sample pushes the timing of the permanent outliers to the second half of 1986.

The explanation for the differences across each method would appear to be straightforward. When including observations from 1986 and 1987 into the analysis, the impact of these values will be incorporated into the coefficient estimates. In examining an individual observation, the outlier-detection routine will be less likely to consider a data point as extreme when that information is already incorporated into the estimation procedure. This is in contrast to the first outlier analysis when coefficient values representing information only through 1985 were imposed on the entire sample. Thus, the information contained in the tail of the sample was not included in the coefficient estimates making it more likely that those observations would be labeled as extreme. Despite this, what was interesting was that in both cases, outliers were detected in 1986 and 1987, although the second set of results were not as strong as the first case. In both of these cases, although the results differed somewhat across methods, the evidence suggests that the composition of the tail of the sample differs from the years prior to 1986, except for some one-time outliers in 1979 and 1982.(7)

A sensitivity analysis was also performed. A critical value of 2.0 was used in the above outlier detection analysis. This corresponds to about a five percent significance level since the statistic has a normal distribution under the null hypothesis. To test for the strength of these results, the critical value was incremented by .25 until it reached 3.5. For C = 2.25, the results did not change. However, for 2.5</=C</=3.00, only the permanent outliers were detected. For C>3.00, the ARIMA (2,1,0), using the 1985 coefficients continued to detect permanent outliers while the other model did not. Again, given the above explanation, we might expect these types of results.8

Conclusion

The telecommunications industry has undergone significant changes over the past few years. These changes have occurred in all areas of the industry. The statistical results presented here would indicate however, that it is only in the past two or three years that evidence of significant changes can be found in industry data that have been very aggregated. Some preliminary testing using data disaggregated across market segments has indicated that structural shifts for particular types of services occurred before 1986.(9)

A number of factors have played a role in this shift. Compared to only a few years ago, an enormous number of services are available. Part of this increase reflects the more sophisticated demands of today's business and residential users. But in addition, technological advancements have made the availability of some of these new services possible. Moreover, interstate rate cuts in recent years have certainly affected overall telecommunications demand. The rate cuts were largely due to changes in the way in which the costs associated with accessing the local telephone networks were allocated among long distance carriers, local telephone companies and consumers. As the access costs paid by the long distance companies have declined, the reductions have been passed on to long distance customers in the form of lower prices.

From an analyst's perspective, it is important to take this information into consideration in any statistical analysis. Previously established relationships most likely will have changed requiring a more careful interpretation of new results.

Given the results presented here, a number of avenues can be further pursued. Additional observations obviously are needed to shed further light on the results presented in this analysis. In particular, separating the impact of the different forces that have been pinpointed as the sources of the structural shift would be useful. In addition, a disaggregated analysis across different services and market segments should prove enlightening.

Footnotes

1. For certain data reasons, only interstate usage was considered in this study. Intrastate usage that is classified as "long distance" was not used. Moreover, private line data and software defined network (SDN) numbers were not included. Data for several of the components of the data series were available through 1988:1. But the last complete data point is 1987:3. Finally, certain assumptions were necessary in developing the appropriate weights needed in order to derive industry THTCCS since its various components may not be the same across all long distance vendors.

2. It is useful to keep in mind that when using first differences, the "base" for the coefficient of determination is really a random walk model. For a description, see Harvey [11]. This approach is suggested when using trending data since the conventional R2 will yeild essentially valueless information.

3. A good explanation of estimation methods and diagnostics can be found in Harvey [10]. For another useful approach in model selection using likelihood ratio tests, see Dickey and Fuller [7] and an application of this methodology in Shugart & Tollison [12].

4. The outlier detection procedure used in this paper differs somewhat from that developed by Tsay. The Tsay methodology is a procedure designed to interpret the data and then replace what it considers to be an outlier. Therefore, the procedure loops through the data step performing as many iterations as there are data points. Outliers are "corrected" and then the model is re-estimated. This results in a refinement of the initial ARIMA estimation that was used to provide the weights used in the transformation of the variables. Because the focus of this paper was on the nature of the structural shifts per se, and not a combined procedure that would "correct" the data as they were being processed, the coefficients from the 1976-1985 estimation were imposed on the entire series and only the outlier detection methodology was employed.

5. My thanks to John Surgent, Staff Supervisor at AT&T, who programmed the iterative routine that was used to make the necessary calculations in the outlier detection procedure.

6. Tsay also notes that this outlier detection methodology is useful in pointing out likely structural breaks and the possible need for estimating different models for different parts of the sample. To a certain extent, the opposite approach is taken here in that large changes in the coefficients prompted the analysis of outliers at those points. This method was used precisely because of the small sample that was available for the analysis.

7. For the sake of comparison, the SAS X11 routine used to deseasonalize data was also applied. Within the routine is the capability of detecting and replacing outliers. This is based on the derivation of an "irregular" series after the trend, cycle and seasonal components have been removed. Extreme deviations from the mean of the irregular series are tagged and adjusted. In turn, the original series is corrected for these extreme irregular values. Using the default values for the determination of outliers and modifying the SAS procedure by requiring it to iterate over each of the observations in the sample, X11 determined that there was an outlier in 82:1, one beginning in 86:3 and continuing through the remainder of the sample. The SAS procedure differs considerably in scope and methodology from the routine developed by Tsay. It is also limited in that it cannot determine the type of outlier that is detected. The size of the outlier calculated also differed somewhat across each method. Nevertheless, it is useful in that it largely confirms the presence and location of outliers that were found using the Tsay method.

8. The complete set of statistics can be obtained from the author.

9. Some tests on total business and total residential markets would indicate that the model specification differs somewhat from market to market. The analysis also indicates a somewhat different timing in terms of the beginning of the presence of outliers.

References

1. Box, G.E.P. and D.A. Pierce. "Distribution of Residual Autocorrelations in Autoregressive-Integrated-Moving Average Time Series Models." Journal of the American Statistical Association, Vol. 65, December, 1970.

2. Box, G.E.P. and G.C. Tiao. "A Change in Level of a Non-Stationary Time Series." Biometrika, Vol.52, 1965, p.181-192.

3. Chang, I. "Outliers in Time-Series." Unpublished dissertation, University of Wisconsin, Madison, Department of Statistics, 1982.

4. and G.C. Tiao. "Estimation of Time-Series Parameters in the Presence of Outliers." University of Chicago, Statistical Research Center, Technical Report 8, 1983.

5. Chen, C. and G.C. Tiao. "Some Diagnostic Statistics in Time Series." University of Chicago, Statistical Research Center, Technical Report, 1986.

6. Chow, Gregory. "Tests of Equality Between Sets of Coefficients in Two Linear Regressions." Econometrica, Vol.28, July 1960, p.591-605.

7. Dickey, David A., and W.A. Fuller. "Distribution of the Estimators for Autoregressive Time Series with a Unit Root." Journal of the American Statistical Association, No. 74, 1979, p.1057-1072.

8. , William R. Bell and Robert B. Miller. "Unit Roots in Time Series Models: Tests and Implications." The American Statistician, Vol.40, No.1, February 1986, p.12-26.

9. Fuller, W.A. Introduction to Statistical Time Series. New York: John Wiley, 1976. 10. Harvey, A.C. Time-Series Models. Phillip Allan Publishers, 1981.

11. . "A Unified View of Statistical Forecasting Procedures." Journal of Forecasting, Vol. 3, 1984, p.245-275.

12. Shugart, William F. and Robert D. Tollison. "The Random Character of Merger Activity." The Rand Journal of Economics, Vol.15, No.4, Winter 1984, p.500-509.

13. Tsay, Ruey S. "Time-Series Model Specification in the Presence of Outliers." Journal of the American Statistical Association, Vol.81, 1986, p.132-141.

14. . "Outliers, Level Shifts and Variance Changes in Time Series." Journal of Forecasting, Vol.7, No.1, 1988, p.1-20.

Introduction

Enormous changes have occured in the telecommunications industry over the past decade. Obviously, one of the biggest events was the breakup of the Bell System which occured in January 1984. But a number of other changes have also taken place. The emergence of alternative providers and the wholesale introduction of new services have given customers increased choices and flexibility to meet their long distance needs. In addition, technological advancements resulting in such services as integrated services digital network (ISDN) promises to open up new opportunities in long distance provisioning. Moreover, as the structure of the U.S. economy changes, so does the use of telecommunications in the industrial process. Data transmission and the ability of computers to communicate over long distance networks have become increasingly important. As business needs have changed, long distance no longer means simply making a telephone call.

Therefore, from both the buying side and the selling side, it can be seen that the industry is changing. Given this, a natural avenue of inquiry might be to ask if statistical evidence of these changes can be found. In other words, does an analysis of the data indicate that such shifts are occurring and what is the nature of these shifts? Knowledge of this would validate the view that the telecommunications industry is undergoing the large scale transformation that has long been predicted. This information would also be useful from an analytical perspective when studying the various types of statistical and economic relationships that are found in telecommunications. Changes in the nature of these relationships would require that this new information be taken into account when generating forecasts or analyzing various issues that affect the telecommunications industry.

Methodology and Data

A strictly time-series approach was utilized here. That is, no economic or price data were used. The intent was to focus solely on the data series itself and to also take advantage of some recent advances in the analysis of time-series data. The series that was analyzed consisted of quarterly interstate volumes for the entire telecommunications industry. This included all interstate services across all long distance carriers. The series was then converted to total holding time in hundred call seconds (THTCCS). THTCCS is an internal AT&T measure of network utilization which includes such characteristics as call set-up time. For a number of applications, it is considered the most relevant measure of the demand that is placed on a network. The data series ran from 1976:1 through 1987:3.(1)

Since the purpose of this paper was to focus on structural changes in the telecommunications industry, a natural place to start was with divestiture which began on January 1, 1984. Therefore, we first considered a sample running from 1976 through 1983. Given this, the next step was to derive the model specification that best represented the series over that interval. In initial estimations, convergence problems often occurred when including moving-average components in the equation. Consequently, moving-average terms were eliminated from subsequent regressions. When the series was measured in levels, an examination of its autocorrelations suggested that the data was nonstationary. Consistent with this was that the estimation of simple ARIMA models indicated the possibility of unit roots. We then formally tested for the presence of unit roots. In other words, in the simple formulation, (1) Y sub t = a + bY sub t-1 + e sub t we wanted to test the null that b = 1. In this case, conventional asymptotic distribution theory could not be applied. Dickey develops an alternate distribution for b. Under the null hypothesis, it has "tau-distribution" that is not the standard t-distribution. The distribution of the tau-statistic was generated using a computer simulation developed by Fuller [9]. An alternative way of expressing the above formulation can be seen by subtracting Y(t-1) from both side giving us the expression, (2) Delta Y sub t = a + (b-1)Y sub t-1 +e sub t.

In other words, a test for the presence of a unit root requires regressing first differences on the lagged level value of the dependent variable and testing for its significance. Lagged first-differenced variables can also be included and tested for significance. Dickey and Fuller [7] show that (b-1) has a tau-distribution. This makes testing for a unit root straightforward in that we can use the ratio of the coefficient and standard error for the lagged level term and compare this statistic with the distribution table prepared by Fuller.

In this case, (b-1)=-.007 with a standard error of .017. Therefore, the tau-statistic was -.007/.017 = -.41. Comparing this to a critical value of -2.93 at the five percent level of significance, we found that this was not significant and we did not reject the null that b = 1. Therefore, modeling in first differences was an appropriate course of action. A similarly constructed test rejected the use of second differences. Given that we could not reject the hypothesis of first differences, we then systematically tested for the optimal lag length using standard t-tests. The t-statistics for lags three through six were less than one and therefore rejected. The final accepted result was: (3) Delta Y sub t = .237 - .413 Delta Y sub t-1 - .387 Delta Y sub t-2 (.016)(.172) (.173) Q(12)=10.3 AIC=-18.6 SBC=-14.3 R raised to 2=.28

The numbers in parenthesis represent standard errors. The t-statistics indicated that the coefficients were different from zero. A Box-Pierce Q-Test for 12 autocorrelations generated a Q-statistic equal to 10.3 which with nine degrees of freedom was less than the critical value of 21.03 at the five percent level of significance indicating that the residuals were white noise. In addition, the Akaike Information Criterion (AIC) and the Schwartz Bayesian Criterion (SBC) were provided as measures of goodness-of-fit used to compare non-nested alternative model specifications. Of the models tested, this form minimized the SBC while the AIC was the second smallest. Although an ARIMA (3,1,3) minimized the AIC, the ARIMA (2,1,0) specification was clearly superior in terms of the overall diagnostics. The R2=.28 indicated a fairly good fit in first differences.2 In addition, there was little indication of seasonality. The model was estimated using a maximum likelihood method. The results differed little when least-squares methods were employed. Therefore, we found that this formulation was a reasonable representation of the data series relative to other models.3

Structural Change

The possibility of a structural change in the series was then considered. Following Chow [6] and using the ARIMA (2,1,0) functional form, an additional four observations (the year 1984) were added to the sample. In this case, F-tests at the one percent and five percent levels of significance did not lead to a rejection of the null hypothesis of no structural change. The inclusion of four more observations for 1985 also did not change these results. For the sake of comparison, the regression results for the 1976-1985 sample were: (4) Delta Y sub t = .255 - .346 Delta Y sub t-1 - .331 Delta Y sub t-2 (.016)(.156) (.158) Q(12)=11.6 AIC=-23.5 SBC=-18.5 R raised to 2=.179

As can be seen, the coefficients changed relatively little while the fit remained reasonably good. In estimating this sample, we found that this specification minimized the SBC although an ARIMA (3,1,0) model minimized the AIC.

However, when the observations for 1986 were added, the Chow test indicated the likelihood of a structural change in the series. The values of the coefficients dropped and the overall fit deteriorated. And when data through 1987 were used, we saw even larger changes in the coefficients and the model fit. Using the entire 1976-1987 sample and an ARIMA (2,1,0) form resulted in: (5) Delta Y sub t = .311 - .031 Delta Y sub t-1 + .231 Y sub t-2 (.042)(.159) (.160) Q(12)=26.8 AIC=-1.37 SBC=4.1 R raised to 2=.051

As can be seen, the signs and values of the coefficients changed considerably and both lags became insignificant. With an R2 = .051, the fit of this specification deteriorated to the point where it was only marginally better than a random walk model. And with a critical value of 16.9 at the five percent level and 21.7 at the one percent level, we also concluded that the residuals were no longer white noise. A further examination of the series when measured in first differences indicated that its variance increased beginning in 1986.

Therefore, standard tests indicated that from a time-series perspective, the statistical relationship between total long distance telecommunications demand and its lagged values had undergone significant changes. Although divestiture occurred in 1984, the evidence suggests that these aggregate relationships significantly shifted beginning in 1986.

Structural Change and the

Presence of Outliers

In order to more closely examine the type of structural change that the initial regression results suggested, a number of further tests were performed on the data. The tests involved the detection of outlier observations. The basic approach follows the framework developed by Tsay [14] and was modified somewhat for this analysis. Outliers in this case represent anomalous observations not consistent with the whole of the data series. There are more formal definitions, but one simple approach classifies outliers in terms of the number of standard deviations an observation may be from the mean or moving-average. Outliers may take several forms. They could represent a one-time "shock" to the data which occurs because of reporting problems or a one-time event, the impact of which is completed in one period. They can also be a level change in the data which could be the result of a permanent structural shift or perhaps a transitory shock whose impact decays as time increases.

Briefly, there are several steps to the creation of these outlier detection tests. The basic framework was developed by Box and Tiao [2] and further extended by Chang [3], Chang and Tiao [4], Chen and Tiao [5] and Tsay [13]. This method requires the transformation of the data series using the values of the series as well as weights that are based on an initial ARIMA model estimation. These transformed variables are employed in a subsequent regression, the coefficients and standard errors of which are used to create a series of ratio tests that are sequentially applied to every observation in the sample. The null hypothesis is that a particular observation is not an outlier while the various alternative hypotheses consist of the different types of outliers. Under the null, this statistic has a N(0,1) distribution. For more information regarding these tests, see the citations above.

In our approach, since tests for structural change indicated that there were no significant shifts among the coefficients through the end of 1985, this specification and its coefficient estimates were then imposed on the entire series and the individual observations were then systematically tested for the presence of outliers.4 The results of the tests were interesting.5 Outlier observations were detected at three places. The first two represented additive or one-time displacements at 1979:3 and at 1982:1 where total network demand was significantly lower than in adjacent periods. The likely explanation for the drop in 1982:1 was the severe recession with the 1981:4 real GNP declining at a five percent annual rate and 1982:1 showing a six percent annual decline. Economics alone would not seem to be the explanation for the 1979 outlier. There are several other possible explanations including recording problems.

The third represents a series of outliers that were detected beginning in 1986 and continued through the end of the sample. Here, the outlier uncovered was of a permanent nature that indicated that a structural change had occurred in the series. The actual values of the series were significantly higher than the data up to that point would suggest would be reasonable. Unlike the 1982:1 outlier, economic factors do not seem to play a dominant role in explaining the observations seen here. Economic growth rates were modest during this period compared to interstate long distance growth.

By way of an extension of this analysis, when the regressions that were estimated using samples taken from 1976-1983, 1976-1984, and 1976-1986 were tested, outliers were detected at the same locations as those found when using the 1976-1985 sample.

As a result of the tests that were performed on the data, it appears that structural shifts occurred in the values of THTCCS beginning in 1986 with one-time changes occurring in 1979 and 1982.(6) According to the statistical analysis of them, the 1986 values represent permanent shifts in the series.

Another Approach to Outlier Detection

In an attempt to test the above results, a second method was also tried. The methodology that was initially used to derive a suitable model over the 1976-1983 sample was applied to the entire sample. Again, unit root tests indicated that first differences were appropriate. In this case, a random walk model and an ARIMA (4,1,0) model were selected as among the best forms for this series. Although the random walk minimized the SBC, the ARIMA (4,1,0) minimized the AIC. The ARIMA (4,1,0) was finally selected because its goodness-of-fit was superior to the random walk. The complete results for this model were: (6) Delta Y sub t = .36 - .16 Delta Y sub t-1 + .22 Delta Y sub t-2 + .47 Y sub t-3 + .24 Delta Y sub t-4 (.13)(.15) (.14) (.16) (.18) Q(12)=12.2 AIC=-7.4 SBC=1.8 R raised to 2=.245

Given this model, the outlier detection mechanism was applied. There was evidence of an additive outlier in 1979:3 and then a permanent shift beginning in 1986:3. The 1982:1 additive outlier was not detected. In addition, the permanent outliers were not flagged until 1986:3. Consequently, the overall conclusions are roughly the same in terms of the location of the outlier observations, although the use of the 1976-1987 sample pushes the timing of the permanent outliers to the second half of 1986.

The explanation for the differences across each method would appear to be straightforward. When including observations from 1986 and 1987 into the analysis, the impact of these values will be incorporated into the coefficient estimates. In examining an individual observation, the outlier-detection routine will be less likely to consider a data point as extreme when that information is already incorporated into the estimation procedure. This is in contrast to the first outlier analysis when coefficient values representing information only through 1985 were imposed on the entire sample. Thus, the information contained in the tail of the sample was not included in the coefficient estimates making it more likely that those observations would be labeled as extreme. Despite this, what was interesting was that in both cases, outliers were detected in 1986 and 1987, although the second set of results were not as strong as the first case. In both of these cases, although the results differed somewhat across methods, the evidence suggests that the composition of the tail of the sample differs from the years prior to 1986, except for some one-time outliers in 1979 and 1982.(7)

A sensitivity analysis was also performed. A critical value of 2.0 was used in the above outlier detection analysis. This corresponds to about a five percent significance level since the statistic has a normal distribution under the null hypothesis. To test for the strength of these results, the critical value was incremented by .25 until it reached 3.5. For C = 2.25, the results did not change. However, for 2.5</=C</=3.00, only the permanent outliers were detected. For C>3.00, the ARIMA (2,1,0), using the 1985 coefficients continued to detect permanent outliers while the other model did not. Again, given the above explanation, we might expect these types of results.8

Conclusion

The telecommunications industry has undergone significant changes over the past few years. These changes have occurred in all areas of the industry. The statistical results presented here would indicate however, that it is only in the past two or three years that evidence of significant changes can be found in industry data that have been very aggregated. Some preliminary testing using data disaggregated across market segments has indicated that structural shifts for particular types of services occurred before 1986.(9)

A number of factors have played a role in this shift. Compared to only a few years ago, an enormous number of services are available. Part of this increase reflects the more sophisticated demands of today's business and residential users. But in addition, technological advancements have made the availability of some of these new services possible. Moreover, interstate rate cuts in recent years have certainly affected overall telecommunications demand. The rate cuts were largely due to changes in the way in which the costs associated with accessing the local telephone networks were allocated among long distance carriers, local telephone companies and consumers. As the access costs paid by the long distance companies have declined, the reductions have been passed on to long distance customers in the form of lower prices.

From an analyst's perspective, it is important to take this information into consideration in any statistical analysis. Previously established relationships most likely will have changed requiring a more careful interpretation of new results.

Given the results presented here, a number of avenues can be further pursued. Additional observations obviously are needed to shed further light on the results presented in this analysis. In particular, separating the impact of the different forces that have been pinpointed as the sources of the structural shift would be useful. In addition, a disaggregated analysis across different services and market segments should prove enlightening.

Footnotes

1. For certain data reasons, only interstate usage was considered in this study. Intrastate usage that is classified as "long distance" was not used. Moreover, private line data and software defined network (SDN) numbers were not included. Data for several of the components of the data series were available through 1988:1. But the last complete data point is 1987:3. Finally, certain assumptions were necessary in developing the appropriate weights needed in order to derive industry THTCCS since its various components may not be the same across all long distance vendors.

2. It is useful to keep in mind that when using first differences, the "base" for the coefficient of determination is really a random walk model. For a description, see Harvey [11]. This approach is suggested when using trending data since the conventional R2 will yeild essentially valueless information.

3. A good explanation of estimation methods and diagnostics can be found in Harvey [10]. For another useful approach in model selection using likelihood ratio tests, see Dickey and Fuller [7] and an application of this methodology in Shugart & Tollison [12].

4. The outlier detection procedure used in this paper differs somewhat from that developed by Tsay. The Tsay methodology is a procedure designed to interpret the data and then replace what it considers to be an outlier. Therefore, the procedure loops through the data step performing as many iterations as there are data points. Outliers are "corrected" and then the model is re-estimated. This results in a refinement of the initial ARIMA estimation that was used to provide the weights used in the transformation of the variables. Because the focus of this paper was on the nature of the structural shifts per se, and not a combined procedure that would "correct" the data as they were being processed, the coefficients from the 1976-1985 estimation were imposed on the entire series and only the outlier detection methodology was employed.

5. My thanks to John Surgent, Staff Supervisor at AT&T, who programmed the iterative routine that was used to make the necessary calculations in the outlier detection procedure.

6. Tsay also notes that this outlier detection methodology is useful in pointing out likely structural breaks and the possible need for estimating different models for different parts of the sample. To a certain extent, the opposite approach is taken here in that large changes in the coefficients prompted the analysis of outliers at those points. This method was used precisely because of the small sample that was available for the analysis.

7. For the sake of comparison, the SAS X11 routine used to deseasonalize data was also applied. Within the routine is the capability of detecting and replacing outliers. This is based on the derivation of an "irregular" series after the trend, cycle and seasonal components have been removed. Extreme deviations from the mean of the irregular series are tagged and adjusted. In turn, the original series is corrected for these extreme irregular values. Using the default values for the determination of outliers and modifying the SAS procedure by requiring it to iterate over each of the observations in the sample, X11 determined that there was an outlier in 82:1, one beginning in 86:3 and continuing through the remainder of the sample. The SAS procedure differs considerably in scope and methodology from the routine developed by Tsay. It is also limited in that it cannot determine the type of outlier that is detected. The size of the outlier calculated also differed somewhat across each method. Nevertheless, it is useful in that it largely confirms the presence and location of outliers that were found using the Tsay method.

8. The complete set of statistics can be obtained from the author.

9. Some tests on total business and total residential markets would indicate that the model specification differs somewhat from market to market. The analysis also indicates a somewhat different timing in terms of the beginning of the presence of outliers.

References

1. Box, G.E.P. and D.A. Pierce. "Distribution of Residual Autocorrelations in Autoregressive-Integrated-Moving Average Time Series Models." Journal of the American Statistical Association, Vol. 65, December, 1970.

2. Box, G.E.P. and G.C. Tiao. "A Change in Level of a Non-Stationary Time Series." Biometrika, Vol.52, 1965, p.181-192.

3. Chang, I. "Outliers in Time-Series." Unpublished dissertation, University of Wisconsin, Madison, Department of Statistics, 1982.

4. and G.C. Tiao. "Estimation of Time-Series Parameters in the Presence of Outliers." University of Chicago, Statistical Research Center, Technical Report 8, 1983.

5. Chen, C. and G.C. Tiao. "Some Diagnostic Statistics in Time Series." University of Chicago, Statistical Research Center, Technical Report, 1986.

6. Chow, Gregory. "Tests of Equality Between Sets of Coefficients in Two Linear Regressions." Econometrica, Vol.28, July 1960, p.591-605.

7. Dickey, David A., and W.A. Fuller. "Distribution of the Estimators for Autoregressive Time Series with a Unit Root." Journal of the American Statistical Association, No. 74, 1979, p.1057-1072.

8. , William R. Bell and Robert B. Miller. "Unit Roots in Time Series Models: Tests and Implications." The American Statistician, Vol.40, No.1, February 1986, p.12-26.

9. Fuller, W.A. Introduction to Statistical Time Series. New York: John Wiley, 1976. 10. Harvey, A.C. Time-Series Models. Phillip Allan Publishers, 1981.

11. . "A Unified View of Statistical Forecasting Procedures." Journal of Forecasting, Vol. 3, 1984, p.245-275.

12. Shugart, William F. and Robert D. Tollison. "The Random Character of Merger Activity." The Rand Journal of Economics, Vol.15, No.4, Winter 1984, p.500-509.

13. Tsay, Ruey S. "Time-Series Model Specification in the Presence of Outliers." Journal of the American Statistical Association, Vol.81, 1986, p.132-141.

14. . "Outliers, Level Shifts and Variance Changes in Time Series." Journal of Forecasting, Vol.7, No.1, 1988, p.1-20.

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Author: | Szmania, Joe |
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Publication: | Review of Business |

Date: | Mar 22, 1989 |

Words: | 3951 |

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