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Investigating Predictability of Different "Forms of Return" in Tehran Stock Exchange: Some Rolling Regressions-based Evidence.

Introduction

Researchers for various reasons, such as finance-behavioral theories or absence of full market efficiency, have considered stock returns to be predictable, and for many years (for example, Dow, 1920) have attempted to identify the nature and elements of its formation. This article is also on this topic and tries to investigate the predictability of the stock returns in Iranian texture.

So far several models, such as Ou & Penman (1989), Fama & French (1993), Zhang (2002), Fama & French (2015), have been proposed, in order to predict capital market company's returns, but all of these models originate in other countries and there is evidence that the returns related models are not accurately applicable in different countries (Griffin, 1997; Thomsen, 2010). Furthermore, the elements of the variables that form the models change over time (Sheari, 2004; Abbaszadeh & Golestani, 2010; Paye & Timmermann, 2006) and people with different investment horizons participate in the market. Each of them focuses on aspects of returns. For example, while a short-term investor is interested in information about next year returns, mid-term and long-term investors are also likely to pay attention to the aggregate returns. Therefore, in addition to country-specific predictive models, prediction of each type (form) of returns, by meeting the information needs of a particular range of investors, will be beneficial.

These reasons and paying attention to the conditions of Iran, such as double-digit inflation, unusual downturns and booms in alternative markets and special political conditions raised this possibility that variables related to the returns in Iran are different from other countries and motivated us to design Iranian specific stock returns models. Specifically, in this research it has been attempted to investigate the predictability of some forms of returns, including three forms of aggregate returns (as the representative of the midterm returns), next year returns (as the representative of the short-term turn) and one year delayed returns (as a factor affecting the inefficiency of the capital market in Iran).

Usual regression models that are based on data mining techniques tend to look-ahead bias (Zhong & Enke, 2017). Rolling regressions is one of the available methods to test the "application of the models in practice", and is rooted in the concept of "out of sample" analysis (Thomsen, 2010). In the process of rolling regressions, it is assumed that the person is in the real world and at any time (year), using all the available information, designs his/her model and predicts the future; therefore, using this method will reduce the data mining problems. We design, compare, test, and rank models with the "out of sample" analysis based on rolling regressions technique to prepare a comprehensive analysis of stock returns predictability in Iranian texture. Comprehensiveness of the present research about the analysis of several forms of returns and the use of rolling regressions in models validation are considered as our contribution to the literature.

Our paper now proceeds as follows. We discuss the theoretical foundations of the work in the following section. In next three sections we first explain the data and analysis methods then design validate and rank our models. Finally, a summary of results and conclusions are presented.

Theoretical Foundations

Arbitrage Pricing Theory

Arbitrage pricing theory (APT) is a well-known method of estimating the price of an asset. The theory assumes an asset's return is dependent on various macroeconomic, market and security-specific factors. The general idea behind APT is that two things can explain the expected return on a financial asset: 1) macroeconomic/security-specific influences and 2) the asset's sensitivity to those influences. This relationship takes the form of the linear regression formula. In general, using the assumptions of (APT) provides sufficient backing to predict stock returns with a set of relevant variables. Some researchers predict stock returns based on this theory. (Valizadeh, (2014), Namazi & Mohammad Tabar Kasegari, (2007) and others)

Literature review

Despite numerous researches, systematic efforts to design the forecast models of returns in Iran are limited. Valizadeh (2014) in his doctoral thesis has presented a model for predicting next year stock returns. She used confirmatory factor analysis to confirm the initial structure of her data and presented her model with the "specific to general" regression technique. In her model, there was a combination of economic, corporate and market variables. She claimed to have presented a model for explaining next period stock returns.

Ali Mohammadi et al. (2015) presented a model for forecasting current and next year returns using financial ratios. They used the "decision tree" approach to design their model and stated that "decision tree" approach is applicable in model designing.

Recently, Setayesh & Kazemnejad (2016) in their research initially acted to form models for forecasting the returns and then compared the models with each other. They initially identified 52 variables and then ranked them by correlation and relief techniques, and finally, they used seven variables that had the most relationship to returns as variables in their models (Judicial Approach).Their results showed that the use of ensemble models predicts returns better than simple models.

Welch & Goyal (2008) after a massive review of the US capital market found that "out of sample" evidence (rolling regressions) does not confirm the predictability of returns. Campbell & Thompson (2007) applied some limitations in the calculations of these researchers and rejected their result by achieving weak but significant evidence.

Thomsen (2010), Zhou & Faff (2017), and others provided "out of sample" evidence and confirmed "out of sample" predictability of returns.

A review of domestic researches on the modeling of stock returns highlights two points: First, domestic investigations conducted to date often rely on internationally known models such as Fama & French (1993), and the efforts on modeling the returns based on country specific characteristics are limited. Researchers often analyze one or two forms of returns and a comprehensive review of different forms of returns with a vast data set has not been considered.

So in this study, the following question and related hypotheses are tested:

1. By observing the principles of General to specific procedure in modeling, what are the best models (combination of variables) for predicting each form of stock returns in Iran?

To answer this question, 120 sub hypotheses are tested (24 variables in 5 models). One example of these hypotheses is as follows:

H0: There is a significant relationship between "assets growth" and one period future returns.

The second highlighted point is about researches' techniques. Despite much evidence regarding the application of the rolling regressions techniques to validate regression models in international studies, this subject has not been considered in domestic researches. Domestic researchers often rely on in-sample testing of their models, and there is no strong experimental evidence in models validating based on "out of sample" evidence. So in this study, a second question and group of hypotheses are tested.

2. Do designed models have "out of sample" validity?

To answer the second question, we apply "out of sample" approach and test the hypothesis below for each kind of returns :

H0: Based on the pattern of rolling regressions in the "out of sample" validation technique, for "each form of the returns", the errors of the "historical mean model" are less than or equal to the errors of designed model.

The term "each form of returns" means five forms of returns that are investigated in this study. (See last 5 rows of table 1).In the end, as the complimentary information model is ranked based on Theil (1966) measures of accuracy and quality.

Methodology

Sample and Data

Listed and active companies in Tehran Stock Exchange have formed the statistical population of the research. In this research, sampling has not been performed, and only the companies that have following situations have been omitted from the studied population:

1. Investment companies and banks were omitted from the studied population.

2. The companies that their end of the fiscal year does not fit into the real year, as well as those companies that changed the fiscal year during the years studied, were omitted from the surveys.

3. Unprofitable companies have been omitted from the studied population.

4. Companies that due to reasons such as the lack of trade throughout the year, temporary closeness, withdrawal from the stock exchange, and other reasons had no suitable data for analysis were omitted from the investigations.

Finally, by applying the above conditions, the studied companies were limited to 68 companies. In this research, the analyses have been conducted annually, and the beginning of the period under consideration is returned to one year after the required period for the establishment of accounting standards of Iran (2001) and specifically, this period includes years from 2002 to 2015 (14 years). Required data were extracted from professional software (Novin Software) and other credible sources of information, such as the Stock Exchange library and official Cite on Iranian national bank. Excel 2010, Eviews 9 and Stata 14 software were used to analyze the data.

Research Variables

Research variables were identified by a deep study of the literature both inside and outside the country. These variables include 47 variables, which are based on the three fields of company, market, and economy. Definitions and descriptive statistics for all variables (47 independent and five dependent variables) have been presented in Table 1. In this table, large numbers are presented in thousands of billions of Rials.

Due to a large number of research variables, the use of the symbol will be confusing; so in this table, for each variable, a code has been introduced which variable will be identified with throughout the paper. To limit the effect of outliers, the variables have been winsorized at the 5% level of upper and lower limits.

Data analysis method

The method used in this research is the descriptive-correlational type. Designing approaches to regression models and rolling regressions approaches has been used in the panel data context.

The method of conducting the research was as follows. First, the variables that have theoretical relation with returns were identified with a thorough study of the literature. Subsequently, using the "Principle Components Analysis" technique, the volume of initial data set was reduced to make possible the design of the models with "general to specific" (GS) approach. Then, the most suitable predictive model was designed using the mentioned approach, for each form of returns and finally, extracted models were validated using an "out of sample" approach based on rolling regressions and ranked based on the forecast accuracy and quality.

Designing a model in econometrics

In econometrics, two "specific to general" (SG) and "general to specific" (GS) methods have been proposed for designing a model and selecting among many variables (Aflatuni, 2014). The basis for doing the work in the "SG" method is to arrive from a basic and simple model to the ultimate and powerful model. Hendry and Richard (1982) in addition to presenting the criticisms to "SG" method presented the "GS" approach (Armstrong, 2001). In this approach, the researcher starts the work with a comprehensive model that consists of all the variables that affect the studied subject. The mentioned model is fitted and proper validation tests are carried out to determine its reliability. Then, it is tried to simplify the model and provide a final model by omitting variables that are not statistically significant.

Principle component analysis

So far, the literature on stock returns has introduced about 50 variables related to returns (Setayesh & Kazemnejad, 2016). Using all of these variables in the primary regression of "GS approach" is not possible for two reasons; first, co-linearity will exist between some of the variables and second, excessive reduction of the degree of freedom might be prevalent. Therefore, it is necessary to use valid data-reduction methods to reduce the initial number of variables to an acceptable level. Sorzano et al. (2014) stated that among the techniques for reducing data dimensions, the "Principal component analysis" (PCA) method and its various versions are simpler and more comprehensible than other methods. Hargreaves and Mani (2015), Wang & Choi (2013) successfully used the (PCA) method for data reduction of variables affecting stock returns. In the "PCA" method, by applying the concepts of "Eigen values" and "Eigen vectors", several correlated variables are converted to one (or several) un-correlated component(s) and thus, in the final analysis, the volume of data decreases. In this study, we used "PCA" to reduce our variables.

"Out of sample" analysis based on rolling regressions

Various researchers such as Campbell and Thompson (2007), Thomsen (2010), Bahrami et al. (2016) and others, have used "out of sample" methods to perform the generalizability of models with more reliability.

Rolling regressions technique (RR) is rooted in the concept of "out of sample" analysis. The method of doing the work is that at first, the study period T is divided into two categories, including the "First Period to Period F" and "Period F to Period T" (Equal or Non-equal). Typically, the "first period to period F" is called in-sample period, and the second period is called the "out of sample" period. Then, the returns and so the errors of each year of ""out of sample"" period are calculated and finally, by comparing the errors of the designed model with a benchmark model, predictability of the designed model is concluded.

The estimate of the returns and errors for each year of the "out of sample" period is as follows: first, with the data of in sample-period (first period to period F), the first regression equation is estimated and the returns of the F + 1 period is forecasted. Then, by decreasing the real returns from the forecasted returns, the errors of period F + 1 is calculated. Then the estimation window is stepped forward one period and with data related to the "first period until period F + 1" the second regression equation is estimated and used to forecast the returns and errors of the F + 2 period with the same pattern of the previous period; this approach continues until the last examined period (period T).

The model that has been used in this research as the benchmark model is "historical average returns model". This model usually used as the benchmark model in returns related research. Welch and Goyal (2008), Campbell and Thompson (2007) and Thomsen (2010) and many others used this model as their benchmark model. The main concept of the "out of sample" approach has been depicted in Table 1. In this fig, the period 2002 to 2005 is the in-sample period and the periods 2006 to 2015 are considered as the "out of sample" periods.

"Out of sample" tests

"Out of sample" R squared

The determination coefficient (R2) determines the statistical significance of the models based on the "out of sample" period. This coefficient is calculated from equation 1 (Thomsen, 2010; Welch & Goyal, 2008):

[mathematical expression not reproducible] (1)

In this model, r ( u,F+i) is the forecasted returns based on the designed model and r (r,F+i) is the forecasted returns by the benchmark model. The decision rule is that if the calculated coefficient is greater than zero, it means that the designed model has had a forecasted mean squared error less than the historical model and can be used as a forecasted model.

McCracken (2007)

The test of McCracken (2007) is a famous test at the time of comparing nested models. The confirmation of the null hypothesis of McCracken test (2007) means that the designed model has no suitable forecast ability. In this research, this test has been used for comparison of the designed (unrestricted) and benchmark (restricted) models.

Theil measures (1966)

Also, in this research, two Theil accuracy coefficient (TIC) and Theil quality coefficient (TIC-UII) have been used to rank the models. According to the formula, the value of these coefficients had been between zero and one, and as much the number of these criteria to be closer to zero, the model has better forecast accuracy and quality (Hartmann et al. 2014). In Theil s models (equations (2) and (3)), y it is the actual return on the company (i) in the year (t) and (y it ) is the predicted return of the same company and the same year and n is the number of observations.

[mathematical expression not reproducible] (2)

[mathematical expression not reproducible] (3)

Besides these criteria, a various set of statistical criteria has been used to achieve the reliable results. These methods and criteria have been presented in summary in table 2.

Research results

Determining the final set of research variables with PCA

The final result of applying the "PCA" method is the conversion of 27 variables (more than 50%) to five independent components. The results have been obtained after applying all necessary tests which have been mentioned in the first panel of table 2. Final estimation equation of each component has been presented in Table 3. Simply, these equations are composed of highly correlated variables (based on PCA concepts) and are used to estimate the number of each component. The estimated components then have been replaced by the constituent variables in the analysis.

The numbers inside the square are variable codes which have been presented in Table 1

The components are composed with 19 other variables, (collectively 24 variables) the final set of variables used in the design of forecast models.

Designing forecast models with a general to specific approach

In this phase, first, the stationarity of variables was tested by Levin, Lin & Chu measure and then in total, by fitting and modifying the fifteen regression equations, the final model of all forms of returns (five forms) has been designed. To summarize, in each case only the final model and its initial validation measures (Adj R2 and F Test) have been presented and the equation of the previous levels has not been provided. (Table 4)

The tests used to examine the regression hypotheses are the cases that have been mentioned in Table 2. If necessary, the proposed method of Aflatuni (2016, 316) has been used to correct the regression problems.

Validation of models with rolling regressions technique

Other researchers have used 25 to 50 percent of the data for the initial estimate (Hartmann et al., 2014; Thompson, 2010; Rapach & Wohar, 2006). By considering the nature of our data, the initial estimation window (W) was determined equal to four periods (272 companies -years, 33% of the total data). To do rolling regressions, the expansion period has been set to 1(step=1). Nine forecast equations were formed for each form of returns and in total the returns and errors of the models were predicted and calculated using 45 regression equations. The table 5 shows "out of sample" determination coefficient (R2) and McCracken test of 2007 in the field of comparing the models designed with the historical returns mean. The star sign beside each statistic means the significant of the provided statistics (rejecting the null hypothesis).

In the case of all forms of returns, the null-hypothesis of McCracken test (2007) is rejected; that indicates the superiority of designed models on historical mean based models. The "out of sample" determination coefficient also confirms this matter and indicates that the forecasting power of these models is much higher than that of their own benchmark model. The result of these two tests is that models have more informational value than making the decision based on the mean of returns.

In Table 6, the ranking result of the models has been presented with two criteria of Theil(1966) forecast accuracy and quality. Table 6 shows the "aggregate returns of three periods" which has higher predictability than other forecast criteria. Theil (1966) criteria show relatively good forecast accuracy and moderate forecast quality for models.

Summary and Conclusion

This research has focused on a comprehensive analysis of the predictability of returns forms. The results of the research show that all the different forms of returns are somewhat predictable (a positive answer to the first research question). In total, 17 variables (see table 4), formed forecast models of five forms of returns, and the significant relationship of other variables with returns were rejected. The forecast through all forms of returns will be more effective than the use of the moving average and will produce results with lower error (confirmation of the hypotheses related to second question), so that about most successful forecast model, the designed model error includes only about 38 % of the error in the averaging method. This criterion in the worst case reaches around 57%.(see table 5) However, in the accuracy and forecast quality dimension( the third question of the research), models have acted slightly weaker. In the dimension of forecast quality (UII criteria-table 6), at best form (aggregate return with three-periods), the mean of forecast quality is about 60% and in the worst form (one year delayed returns) is about 40%, which are relatively unsuitable and show the medium(weak) quality of forecasts. From the accuracy point (UI criteria-table 6), the numerical index varies from 68% to 78%, which is relatively acceptable.

Other results that have been obtained from the implementation of this research are discussed below:

1. Almost in all conducted analyses and all metrics computed in this paper (tables 4, 5 and 6), the aggregate returns are superior to single-period returns. The reason for this matter is probably that the aggregate returns, with the sum of the returns of several years, will modify the effect of incidental fluctuations that cause to distort results of forecasts and make forecasts more possible. Given this result, it is suggested that in terms of stability and better predictability of investment in the midterm and long term, sufficient awareness is needed to replace the horizons of longer-term investment with short-term horizons and reduce the effects of stock fluctuations which are nearly common in Iran.

2. Another important result of the present research is the emphasis on the significant role of economic variables of oil, gold, inflation and economy liquidity (volume of money) on the returns of companies. These variables had a significant effect on almost all studied models. Valizadeh (2014) emphasized the importance of these variables by including them in his final model. Also, Sajjadi et al. (2010) and Mashayekhi et al. (2010) and others pointed to the significant relationship between some macroeconomic variables and stock cash returns. In contrast, Namazi & Mohammad Tabar Kasegari (2007) result stated that there is not a significant relationship between economic indexes and the stock returns. However, most of the researches have supported the effect of economic variables on stock index. The results of this research show that the lack of attention to these markets as complementary and substitute markets can encounter regression results with a serious challenge. Therefore, it is recommended that these economic variables be included in the return models so that the research not to be encountered with the omitted variable and more reliable results to be presented. In the international dimension, also several studies such as Rangvid (2006); Cooper & Priestley (2009); Thomsen (2010); Westerlund et al. (2015) have supported the significant effect of economic variables on the stock returns.

3. The significance of some company-based variables such as "assets growth" or "assets turnover" shows that financial reporting has informational content and can be considered at least as one source of information to the market. Though, the ability of the models in predicting all forms of returns, and specially the significance of momentum variable (code 31) in some models challenges the notions of stock market efficiency. In this matter, additional researches are needed and suggested.

4. The stock data reduction in domestic studies is principally based on judicial approaches and little attention has been paid to valid data mining methods, such as "factor analysis" or "principal component analysis". The result of this research showed that the "principal component analysis" technique could be used in data reduction of effective variables on stock returns in Iran's capital market.

Limitations and Areas for Future Research

This research has been carried out in the absence of any significant limitations and the results can be expanded in different aspects such as limiting the components identified by the factor analysis approach, comparing different methods of designing the regression models in econometrics and applying valid data reduction approaches such as "principal component analysis" or "factor analysis" to the other important variables of the capital market such as dividend growth and cost of capital.

References

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Azam Mohtadi (1) & (2*), Rezvan Hejazi (1), Sayed Ali Hosseini (1), Mansoor Momeny (3)

(1.) Accounting, Faculty of Social Sciences and Economics, AL Zahra University, Tehran, Iran

(2.) Accounting, Department of Management, Economic and Accounting, Payame Noor University, Tehran, Iran

(3.) Industrial Management/ Faculty of Management, University of Tehran, Tehran, Iran

(Received: December 2, 2017 * Revised: August 23, 2018; Accepted: September 12, 2018)

(*) Corresponding Author, Email: a_Mohtadi@yahoo.com

DOI: 10.22059/IJMS.2018.242990.672848
Table 1. Descriptive information and operational definitions of research
variables Large numbers are presented in thousands of billions of Rials.

        Variable
code    Symbol                       Operational definition

                                     Number of shares x
 1      Market Value                 Share value
                                     (Total assets - Cash
 2      Accrual Items                &investments) - (Total
                                     debts- Current debts)
        Return on
 3      Assets                       Net income /Total assets
        Return on                    Net income/Working
 4      Working                      capital
        Return on                    Net income/Stock holders'
 5      Equity                       equity Systematic risk measure
 6      Beta                         ([cov.sub.i,m]/[var.sub.m])
                                     Cash and its [equivalents.sub.t] -
 7      Cash                         Cash and its [equivalents.sub.t-1]
        Current
 8      Value                        Market [value.sub.t] - Market
                                     [value.sub.t-1]
                                     Total assets
 9      Total Assets
10      %Income
        %Operational                 Net income/Sales
11      Profit                       Operational profit/Sales
        Consumer
12      Price                        ([CPI.sub.t] - [CPI.sub.t-1])
        Index(CPI)                    /([CPI.sub.t-1])
                                     (Average of Gold [Prices.sub.t]-
        Gold                         Average of Gold [Prices.sub.t-1])/
13      Price
                                     (Average of Gold [Prices.sub.t-1])
                                     (Average of Oil [Prices.sub.t] -
14      Average                      Average of Oil [Prices.sub.t-1])/
        of Oil Prices                (Average of Oil [Prices.sub.t-1])
                                     Dividend per
15      %Payout Ratio                share/Earnings per share
                                     Percentage of shares
                                     owned by banks, financial
        %Institutional               institutions, Insurance
16      Investors                    companies, and all real
                                     and legal persons, with
                                     more than 5% of shares.
        % Un-                        1- % Institutional
17      Institutional
        Investors                    investors
        Non-                         1-Percentage of shares
18      Governmental                 owned by government
        Public                       agencies
        Ownership
19      Assets Growth                ([TA.sub.t] -[TA.sub.t-1])
                                     /([TA.sub.t-1])
20      Sales Growth                 ([Sales.sub.t] -[sales.sub.t-1])
                                     /([Sales.sub.t-1])
        Net Working                  Current assets - Current
21      Capital                      liabilities
                                     Sales - The cost of goods
22      Operational                  sold - Other operational
        Profit(Loss)                 expenses
        Income After
23      Tax                          Net income after tax
        Income Before
24      Tax                          Net income before tax
        % Net to Gross
25      Income                       Net income/gross income
        Dividend per                 Dividend/Number of
26      Share(Rials)                 outstanding shares
27      Earnings Per                 Net income/Number of
        Share(Rials)                 outstanding shares
                                     Earnings per [share.sub.t] /Price
28      [E/P.sub.(t-1)] Ratio        of a [share.sub.t-1]
                                     Dummy variable which
                                     takes 1 when a company
29      Group                        is member of a
        Membership                   commercial group and 0
                                     otherwise
        Price to Sales               Share Price/Sales per
30      Ratio                        capita
        Total Assets                 Daily Sales/Average total
31      Turnover                     assets
                                     Dummy variable which
                                     takes 1 when a special
32      Family                       family has more than 20
        Membership                   % of a company's shares
                                     and 0 otherwise
                                     Dummy variable which
                                     takes 1 when net income
33      Momentum                     of a company is more than
                                     last year and 0 otherwise
                                     Interest expenses/Total
34      Interest Rate Effective Tax  debts
35      Rate                         Tax expenses/Total sales
                                     Current assets (except
                                     inventories and
36      Quick Ratio                  investments)/Current
                                     liabilities
        Book to                      Book value of firm
37      Market Ratio                 /Market value of firm
38      Debt Ratio                   Total debts/Total assets
        Debt to Equity               Total debts/Stock holders'
39      Ratio                        equity
                                     Current assets/Current
40      Current Ratio                liabilities
        Current Assets
41                                   Current assets/Fix assets
        Ratio                        Dividend per
42      Dividend-Price               Share/Market value per
        Ratio                        share
        Price-Earning                Market value per
43      Ratio                        share/Earnings per share
                                     Earnings per
44      Earnings-                    Share/Market Value per
        Price Ratio                  Share
                                     Days with at least one
45      Liquidity                    deal/total trading days of
                                     the market.
46      Cash Flows                   Operational cash flows
        Volume                       (The average of [Vom.sub.(t)] -
47      of Money                     The average of [Vom.sub.(t-1)])/
        (VOM)                        The average of [Vom.sub.(t-1)]
                                     The returns on common
Rt+1    Returns of the               stock during the next year
        Next Year                    (period t+1)
        One Year                     The returns on common
Rt+2    Delayed                      stock during the second
        Returns                      next year (period t+2)
        Aggregate                    The sum of the current
Rcom2   Returns 1                    and next year returns
                                     The sum of the current
Rcom3   Aggregate                    and two next years'
        Returns 2                    returns
        Aggregate                    The sum of the two next
Rcom2R  Returns 3                    years' returns


code    Mean     Std      Max     Min

 1         1.03    1.60    6.95     0.06
 2         0.84    1.10    4.73     0.08
 3         0.16    0.11    0.40     0.02
 4         0.47    1.72    4.10    -3.57
 5         0.41    0.22    0.85     0.07
 6         0.39    0.93    2.46    -1.03
 7         0.06    0.025   0.08    -0.05
 8         0.18    0.61    2.20    -0.94
 9         1.03    1.45    6.35     0.09
10         0.22    0.17    0.67     0.02
11         0.26    0.15    0.61     0.05
12         0.19    0.08    0.35     0.10
13         0.30    0.23    0.80    -0.09
14         0.15    0.17    0.38    -0.56
15         0.69    0.26    1.00     0.10
16         0.77    0.17    0.970    0.26
17         0.23    0.17    0.73     0.03
18         0.11    0.31    1.00     0.00
19         0.21    0.19    0.62    -0.07
20         0.24    0.27    0.92    -0.22
21         0.13    0.25    1.00    -0.33
22         0.19    0.27    1.18     0.009
23         0.16    0.27    1.17     0.006
24         0.19    0.30    1.32     0.007
25         0.62    0.23    1.35     0.13
26       860     845       3.018   30
27      1118     933       3.433  119
28         0.20    0.12    0.46     0.031
29         0.74    0.44    1.00   000
30         1.73    1.48    5.69     0.28
31         0.81    0.30    1.45     0.23
32         0.15    0.36    1.00   000
33         0.68    0.47    1.00   000
34         0.05    0.03    0.13   000
35         0.03    0.03    0.10   000
36         0.79    0.34    1.67     0.26
37         0.57    0.38    1.4      0.13
38         0.62    0.14    0.83     0.31
39         2.01    1.20    4.97     0.45
40         1.29    0.46    2.47     0.59
41         0.66    0.17    0.89     0.28
42         0.13    0.07    0.28     0.01
43         7       3.88   19.6      2.7
44         0.1     0.08    0.37     0.05
45         0.04    0.02    0.08     0.01
46         0.13    0.21    0.91    -0.02
47         0.19    0.34    0.39    -0.9
Rt+1       0.36    0.63    2.13    -0.32
Rt+2       0.37    0.65    1.95    -0.48
Rcom2      0.80    0.93    3        -.36
Rcom3      1.27    1.09    3.57     -.025
Rcom2R     0.79    0.93    2.97    -0.36

Table 2. Summary of Tests Used in this Research

Goal(s)                  General
                         Technique(s)

                          Principles
 Data Reduction of        component
     Variables             analysis
                          General to
                           specific
  Designing Models       approach in
                          Panel data
                           context
 Robustness Test &
  Basic Validation
 (Goodness of Fit &      Suitable test
Coefficients Overall
    Validation)
                            Rolling
  "out of sample"        regressions in
     Validation            panel data
                            context
                            Rolling
                         regressions in
 Models Comparison         panel data
                           context

Goal(s)                           specific Test(s)


                            Bartlett's test of Sphericity
Data Reduction of           Kaiser-Meyer-Olkin Measure of
Variables                Sampling adequacy or (MSA measure)
                                  Limier(chow)test
Designing Models                    Breusch-test
                                    hausman Test
                      Unit root>>>>> Levin, Lin & Chu Test(LLC)
Robustness Test &        Collinearity>>>>>Variance inflation
Basic Validation                    Factor (VIF)
(Goodness of Fit &             Homoscedasticity>>>>>>
Coefficients Overall         Breusch- Pagan-Godfrey Test
Validation)                  Serial correlation(SC) >>>>
                             Breusch- Godfrey SC LM Test
                                F test, Adj [R.sup.2]
"out of sample"                     OOS [R.sup.2]
Validation                  McCracken 2007 or MSE-F Test
                               UI Test of Theil(1966)
Models Comparison              UII Test of Theil(1966)

Table 3. final models of components

Optional
Component  models
Name

PPS        Pps = 0.2528 + 0.2842-0.3043+ 0.3244
           [CN.sub.1] = 0.141+ 0.130 + 0.130 + 0.102l + 0.1422
CN1        + 0.1423 +0.1424 + 0.0336 - 0.0338
           - 0.0339 + 0.0340 + 0.1246
           [CN.sub.2] = 0.031 + 0.092 + 0.099 - 0.1121 + 0.0422
CN2        + 0.0223 + 0.0224-0.2536 + 0.27
           + 0.2539 - 0.2840 + 0.0546
           [CPR.sub.1] = 0.143 + 0.135 + 0.1310 + 0.1311 + 0.0715
CPR1       + 0.1025 + 0.1326 + 0.1327 + 0.1130
           + 0.1035 - 0.0937
           [CPR.sub.2] = -0.0033- 0.215 + 0.3810 + 0.2311 - 0.1515
CPR2       + 0.3625 - 0.2726 - 0.2627 + 0.3330
           -0.1335 + 0.3137

Table 5. OOS [R.sup.2] and McCracken (2007) test

Model          MSE F     O[R.sup.2]

[R.sub.com2]   5.60 (*)  0.62
[R.sub.com2R]  5.15 (*)  0.57
[R.sub.com3]   5.12 (*)  0.56
[R.sub.t+1]    5.10 (*)  0.56
[R.sub.t+2]    4.75 (*)  0.53

Table 6. Theil (1966) test results

Model          TIC-UI  TIC-UII

[R.sub..com3]  0.22    0.41
[R.sub.com2]   0.23    0.44
[R.sub.com2R]  0.26    0.48
[R.sub.t+1]    0.32    0.56
[R.sub.t+2]    0.32    0.57
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Author:Mohtadi, Azam; Hejazi, Rezvan; Hosseini, Sayed Ali; Momeny, Mansoor
Publication:Iranian Journal of Management Studies
Article Type:Report
Geographic Code:7IRAN
Date:Sep 22, 2018
Words:6388
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