Dataset

In our study, we investigated the Ramadan Turn Effect in the stock market by converting the Gregorian calendar to the Islamic calendar and mapping it to the stock market. We then constructed a model to identify any findings. Initially, we presented descriptive statistics to analyze the population structure. Subsequently, we conducted pre and post-diagnostics to further strengthen and enhance the usefulness of our research work. Lastly, we conducted a statistical modeling analysis to explore the sensitivity of the Pakistan Stock Market to sovereign indicators, such as Interest Rate, Inflation Rate, and Exchange Rate, by examining the complete linkages between the stock indices and macroeconomic indicators.

We obtained information on all indices recorded as KSE-100 file from "May 25, 1994, to June 28, 2019", KSE All Shares file from "October 17, 2005, to June 28, 2019", KMI All Shares index "May 10, 2016, to June 28, 2019", KSE-30 index "July 31, 2006, to June 27, 2019", and KMI All Share Index from "September 03, 2008, to June 28, 2019". Since most of the indices were generated in the future and comprise a significant portion of the index after their initiation, we have clearly stated the initiation date of each index in the overview section.

We utilized the Equivalent Probability Sampling Method (EPSM) to collect data from accessible and useful sources, ensuring that the sampling process was appropriate and rigorous.

Hypothesis

Statistical Tools and Plan of Analysis

In this study, nonparametric tests such as EGARCH, GARCH, ARCH, and ARCH-LM are used to observe the findings. Anomalies aspects, including rainstorm anomalies, Ramadan peculiarities, Calendar year abnormalities, and leadership style variances, are explored to understand their importance and their relationship with instability in the Pakistan Stock Market.

The presence of these inconsistencies is denoted by 1, while their absence is signified by 0.

To study the Anomalies Effect in the returns of the selected indices, returns were calculated using the following formula:

Where Rt is the day-by-day return of the chosen indices at time t, P(t) denotes the end cost of the Index at timeframe t, and P(t-1) denotes the end cost of the Index at timespan t-1. The augmented Dickey-Fuller test, EGARCH Model, and ARCH LM Test were used to examine the information.

After the stationarity test, the EGARCH model was assessed to examine market differences in the record returns. GARCH family models are more suitable than ordinary least squares (OLS) for analyzing data with inconsistent fluctuations of the error term, such as heteroskedastic data. These models help recognize the highlights of instability in the chosen records' profits (Engle, 2001). The following EGARCH model was assessed for the study.

Equation # 5 (Monsoon Effect)

Equation # 6 (Ramadan Effect)

Equation # 7 (Leadership Style Effect)

Equation # 8 (EGARCH)

Equation 8 represents the constant of the variance equation, where w is the βlog plus the GARCH term (σ2t-1), measuring the group effect in the restricted volatility of the selected indices' returns. The ARCH term α ⌊(Et-1)/(σt-1)⌋ evaluates the proximity and extent of the ARCH influence on the measured conditional fluctuation. The asymmetric effect is evaluated by the γ (Et-1)/(σt-1) expression, which measures the vastness of the asymmetric effect. The estimated EGARCH model coefficients, along with their associated z statistics and p-values, are presented in Table 5; Table 4; Table 3.

As illustrated in Table 1, the KSE-100 covers more than 70% of the capitalization of the entire stock market in Pakistan. Therefore, the volatility in this index would ultimately affect the rest of the indices. Furthermore, the top 30 highest capitalized firms are indexed into KSE-30 and KMI-30, with almost 70% of the companies being the same in both indexes. Thus, any minor or major volatility in the KSE-100 index would affect all four indices. It is noteworthy that the KSE All Share Index has a close association with KSE-100 and reported similar trends. Additionally, KSE-30 and KMI-30 include blue-chip companies that are relatively stable in the stock market, exhibiting low market fluctuations, as demonstrated by their medians of 0.007% and 0.02% and standard deviations of 1.31%, respectively.

Lastly, it is worth mentioning that the KMI-30 and KMI All Share indexes are subject to strict Shariah-compliant policies and regulations. As a result, the KMI All Share reported the least volatile segments in this period, with an average positive return of 0.01% and a standard deviation of 0.98%.

Table 2 shows that the ADF test indicates data stationarity, providing a basis for using ARCH family models. This test is a prerequisite for using such models. In Table 3 we examine the term behavioral finance to investigate whether investors exhibit herding behavior during the Holy Month of Ramadan, when investment and consumption activities are at their peak in Pakistan.

However, the results presented in Table 3 clearly demonstrate that no anomaly has been detected during the Holy Month of Ramadan, as evidenced by the coefficients of each index. The perception was that investors tend to disburse their stocks/securities to meet unusual expenses during Eid-ul-Fitar and other costs associated with Ramadan. However, anomalies were found only in KSE All Shares, which were small and negligible. An anomaly refers to a period (such as a day, a month, or a year) that generates abnormal profits or losses compared to the rest of the months.

Furthermore, ARCH, GARCH, and asymmetry terms are significant for KSE-100, KSE-30, KMI-30, and KMI All Shares returns. The reason to use these econometric techniques is their functions which exactly match our data requirements. GARCH widely applies to various financial time series, including stock returns; GARCH models capture conditional heteroskedasticity by modeling time-varying volatility. They allow researchers to estimate and forecast changing volatility patterns in financial data.

However, GARCH was insignificant for the KSE-100 index at a significance level of 0.05 or 5%, indicating that there are strong clustering features that affect the conditional volatility in each index. The estimated coefficient did not reveal any calendar year anomaly. Moreover, the sensitivity analysis revealed that good news or positive shocks (internal shocks) have a lesser impact on conditional variance than negative news, surprises, or bad information (economic conditions), which tend to have a greater impact on placing volatility in stocks.

Moving forward, the key observable segment in the Table 3 is the asymmetry term, which exhibits strong clustering features of conditional volatility (ARCH Term). ARCH models are suitable for financial time series data where volatility clustering is observed; the ARCH model is the precursor to GARCH and focuses on capturing conditional heteroskedasticity by incorporating lagged squared residuals in the model. It offers a simple way to model time-varying volatility.

This results in persistent fluctuations during the Holy month of Ramadan. However, the estimated coefficient for KSE All Shares return is the only significant one, indicating negative returns recorded during the Holy month. Additionally, ARCH, GARCH, and Asymmetry terms are significant for KSE-100, KSE-30, KMI-30, and KMI All Shares returns. Furthermore, when there is bad information or economic shocks, volatility increases. This leads to an increase in business risk, and investors tend to shift their funds to less risky investments. This is known as the leverage effect.

The prerequisite for employing the EGARCH model is that there should be volatility clustering. EGARCH is particularly useful for modelling financial data that display leverage effects, such as stock returns, where negative market movements tend to result in higher volatility. To diagnose data heteroscedasticity, a residual diagnostic test was applied. The Table 3 shows that the AR (1) p-value is less than 0.05 or 5%, indicating that ARCH family models fit anomaly modelling.

Moving on to Table 4, only two indices had complete data in both regimes. The AR (1) p-value in both classes is less than 0.05, indicating that the ARCH family model can be employed since there is a clustering effect in the mean equation. The ARCH term, GARCH term, and Asymmetry term are significant at 0.05 in both segments, indicating the presence of clustering features in conditional variance in leadership regimes. This segment will be further discussed in a separate head. To diagnose this equation, a validation ARCH-LM test was employed, which is not significant at 0.05. This means that the residuals of EGARCH do not have the ARCH type heteroscedasticity, and the model is fit to explain the findings.

Pakistan experiences a highly dynamic climate environment, with the southern region being hot and lacking the effects of a strong monsoon, while the northern region is enriched with cold-weather snowfall. Over 75% of business activities in Pakistan are concentrated in Karachi City, which is located in the southern region of the country. Despite the unpredictable nature of the stock market weather in Karachi, there is no sequential raining system that can harm business activities.

To explore the volatility clustering features of conditional variance, an AR(1) heteroscedasticity test was employed for each Index, revealing significant results at 0.05 and indicating the need to utilize ARCH family models. The equations for each Index suggest that there are volatility clustering features in the conditional variance, with Table 5 providing insight into how an investor can generate supernormal profits by defeating market anomalies. The estimated coefficient of KSE All Share returns is significant at 0.05, with only negative returns reported in August, while the rest of the months saw positive returns. The table reveals mixed market anomalies, with negative sequential returns observed in August (Volatility Clustering Features).

In Table 6, the critical role of information in market anomalies is discussed. KSE-100 returns reflected negative returns in August, and positive returns in June and September, but no anomalies were detected in July. This anomaly-free month is attributed to critical information that was discovered, as discussed below. Interviews conducted with stock market specialists during the research revealed the significant effect of information on market anomalies, which aligns well with the results obtained from the data in the table. Furthermore, important dates that generate clustering effects in the stock market of Pakistan, such as Board Meetings, Financial Result Announcements, Dividend Declarations, and Dividend Encashment, were classified. The example of HASCOL is used to illustrate how the stock price of the company rises following a Board Meeting (June), continues to rise until the final accounting disclosures (July), and finally experiences a negative anomaly during dividend disbursement (August), as detected in KSE All Shares (Entire Market Volume).

The study highlights the dynamic climate environment in Pakistan and the need to employ ARCH family models to investigate the volatility clustering features of conditional variance. The mixed market anomalies observed in the data suggest the possibility of generating supernormal profits by defeating these anomalies. Additionally, the critical role of information in market anomalies is discussed, with important dates that generate clustering effects identified. Overall, the study provides valuable insights into the stock market in Pakistan and the factors that influence market anomalies.

This study has employed a series of statistical tests to determine the final ARCH family model specification. Initially, descriptive statistics and data stationarity were analyzed, and on backtesting, several models such as OLS, GARCH, TARCH, and EGARCH were statistically driven. The criteria of model selection for the ARCH family model suggested the use of the EGARCH model for developing research findings Table 7.

Undesirable news shocks more as opposed to positive news, good news, and family shocks. Consequently, the term unwelcome news or unpleasant data pertains to a nation's economic disorder. When there are negative earnings in any investment project, it gives investors ample space to rearrange their venture in a risk-free project. To test the compassion of the stock in the framework of Interest Rate (1 Month KIBOR Rate as Proxy), T-Bills Rate (3 Months T-Bills Monthly Rate), and Exchange Rate (Month), the relationship between KSE-All shares and these variables was examined Table 8.

KSE-All is a comprehensive representation of stock trade, comprising all remarkable tradable stocks in the securities exchange. The determined outcomes suggest that KSE-All shares report a negative relationship with the exchange rate. This negative relationship further discourages investors from investing due to the instability of the currency value. Pakistan's stock market is dominated by manufacturing firms, and as a result, import influences the market to a great extent. Therefore, exchange rates act as an essential part of stock records. Moreover, it is further recognized that the Pakistan Stock Exchange is being controlled by a few of the largest local players (Brokerage Houses) who hold around 60% of the entire market. This means that there is a consistent foreign direct investment (FDI) and substantial local funds Table 9.

Moving on to the other remaining indexes, KSE-100 index incomes have no substantial relationship with Interest Rate (Proxy KIBOR) and T-Bill Rates. However, with exchange rate-dependent variables, a significant adverse relationship has been explained in Table 10.

The remaining two indices, KSE-30 and KMI-30, hold a market share of 40.83% and 31.31% respectively, contributing significantly to the overall industry. Therefore, it is reasonable to expect that the results obtained from either of them would be quite similar. Thus, it is presumed that investors are primarily concerned with the exchange rate in every index. However, it is worth noting that while investors in the entire market are sensitive to interest rates and T-bill rates, which signify the shift from risky (equity investment) to risk-free (government or corporate securities) investments, the change in KIBOR has been incorporated in the above-mentioned equation. Furthermore, no autocorrelation has been detected in any of the equations in the estimated model.

In this section, several diagnostic tests were conducted. Table 10 illustrates the correlogram, which demonstrates that there is no serial correlation among the residuals of the estimated equation. Each column in the table represents the results of all five indices with 10 lags. The values displayed are the p-values obtained from the residual diagnostic test in EViews, with the null hypothesis stating that there is no serial correlation among the residuals of the estimated equation. However, while many econometricians do not strongly advocate for normality in ARCH family models, it should be acknowledged that this could be a limitation of the research.