Khalil Ahmad

Some Recently Completed Projects (Business Management) Project-I: Panel Data Regression Analysis EMPERICAL RESULTS Table 1. Correlation Analysis Variables ROCE CR ROCE 1 CR 0.0714 1 QR- RTP -0.5101 -0.0374 PTP 0.0648 -0.2210 ITP - QR RTP PTP ITP 1 -0.0586 -0.1908 -0.0938 - Table 1 provided the degree of relationship between all variables under studies. The positive sign of the correlation coefficient represents direct relationship between indicators while the negative sign is for indirect relationship. There is direct relationship between profitability and CR as the value of correlation coefficient is 0.0714. There is direct relationship between profitability and QR as the value of correlation coefficient is 0.0302. There is indirect relationship between profitability and RTP as the value of correlation coefficient is -0.5101. There is direct relationship between profitability and PTP as the value of correlation coefficient is 0.0648. There is indirect relationship between profitability and ITP as the value of correlation coefficient is -0.2070. Panel Data Regression Model When we need to analyze the data sets with multiple observations of cross-sectional units like profitability and firms over the period of time, we can use panel data that is a branch of time series analysis. Panel data models of two types: 1. Homogeneous panel data models that assume that model parameters are same for all the firms. 2. Heterogeneous panel data models that assume that model parameters vary across firms. The model that I have decided to use for analysis of panel data is (ROCE)it = 0 + 1 (CR)it +  2 (QR)it + 3 (RTP)it +  4 (PTP)it + 5 (ITP)it +  it ; i =1, 2,3,..., N; t = 1, 2,3,...,T; (1) The subscript i in the model is a cross-sectional unit such as a company and t represents the time dimension. Where (ROCE) is return on capital employed our dependent variable, following are independent variables (CR) Current Ratio, (QR) Quick Ratio, (RTP) Receivable Turnover Period, (PTP) Payable Turnover Period, (ITP) Inventory Turnover Period Inventory and  it is the error term. Empirical Panel Data Modeling Empirical model is developed to analyze the impact of working capital management on profitability of the selected companies. For this purpose, panel data of 20 companies recorded from 2015 to 2019 is used to develop this model empirically. After implementation of full model with fixed effects, to capture the heterogeneity and with random effects to capture time component, we have these empirical models: Empirical Model-I (ROCE)it = 27.0906 + 6.9188(CR)it − 7.3996(QR)it − 0.2440(RTP)it + 0.1268(PTP)it − 0.1851(ITP)it (2) i =1, 2,3,...,100; t = 1, 2,3, 4,5 Table 2. Panel Data Regression Full Model with Fixed Effects ROCE Coef. Std. Error t-test P-value 95% Conf. Interval CR- (-15.6654 , 29.5029) QR - - (-37.7528 , 22.9535) RTP - - ( -0.4908 , 0.0028) PTP- ( 0.0437 , 0.2099) ITP - - ( -0.3011 , -0.0689) Constant- ( 8.8343 , 45.3469) F-test P-value R-square- 1 Curriculum Vitae along with Portfolio: Khalil Ahmad 2 The above table showed that the proposed model in equation (1) is highly significant as the p-value is 0.0020 <0.01, 1% level of significance. It explained the overall 22.93% variation as the R-square value is presented there. The empirically estimated parameters of the proposed model are presented as coefficients in the second column of the table 2 which showed that if one unit of CR is increased keeping the effect of other as constant then there will be on average 6.9188 unit increase in ROCE. Similarly, if one unit of QR is increased keeping the effect of other as constant then there will be on average 7.3997 unit decrease in ROCE, if one unit of RTP is increased keeping the effect of other as constant then there will be on average 0.2441 unit decrease in ROCE, if one unit of PTP is increased keeping the effect of other as constant then there will be on average 0.1268 unit increase in ROCE, if one unit of ITP is increased keeping the effect of other as constant then there will be on average 0.1851 unit decrease in ROCE. The interpretation of the constant term is sometime existing, and it is interpreted as there will be 27.0906 units of ROCE if no increment is made in any variable. Table 4. Hausman Test Results ROCE (b) (B) Fixed Effects Random Effects CR- QR -7.3997 -13.8871 RTP -0.2441 -0.3471 PTP- ITP -0.1851 -0.1933 Chi-square P-value- (b-B) Difference - - Std. Error- The results of Hausman test presented in the table 4 suggested the empirical Model-II should be used as the p-value is 0.216 > 0.05. Project-II: Panel Data Regression Analysis Results and Discussions Table 1. Descriptive Statistics of Countries Descriptive Statistics Countries Minimum Maximum Std. Deviation Skewness Kurtosis ROA (in %) Variables 0.660 0.960 0.841 0.087 -0.381 -0.718 ROE (in %) 11.150 17.020 14.052 1.845 0.093 -1.087 5.831 8.056 6.991 0.622 -0.258 0.158 Interest rate -0.257 3.684 1.042 1.222 1.009 0.579 Exchange rate 81.526 101.564 91.257 8.618 0.033 -2.003 - - - 117.403 -0.240 -1.570 -0.877 3.236 1.709 1.187 -1.001 0.879 ROA (in %) 0.790 2.230 1.196 0.225 1.692 7.146 ROE (in %) 10.690 37.200 18.091 4.715 1.283 3.866 3.600 4.672 4.053 0.227 0.231 0.894 -1.402 4.521 1.961 2.227 -0.324 -1.569 6.143 6.770 6.459 0.235 0.021 -1.639 - - - - -0.139 -0.756 Inflation -0.003 8.076 3.291 2.571 0.694 -0.713 ROA (in %) -0.350 0.750 0.171 0.273 -0.370 0.231 ROE (in %) -14.100 18.710 3.284 8.239 -0.898 0.530 8.811 10.354 9.568 0.579 0.043 -1.596 - - - 152.646 -0.382 -1.273 0.522 1.162 0.852 0.250 -0.221 -1.611 ROA (in %) -0.390 0.240 0.022 0.187 -1.325 2.482 ROE (in %) -9.330 9.070 1.511 5.589 -0.563 0.648 Unemployment Canada GDP Inflation Unemployment China Interest rate Exchange rate GDP Unemployment France Mean Interest rate Exchange rate GDP Inflation Germany Curriculum Vitae along with Portfolio: Khalil Ahmad Unemployment 3 3.384 6.966 4.917 1.106 0.444 0.121 92.521 100.000 96.475 2.476 -0.197 -1.060 - - - 210.807 0.121 -1.361 0.646 1.969 1.391 0.436 -0.297 -0.801 ROA (in %) -1.200 0.770 0.188 0.562 -2.175 5.729 ROE (in %) -9.690 8.280 3.039 5.375 -1.865 4.255 Unemployment 8.359 12.683 10.846 1.560 -0.868 -0.394 Interest rate 1.766 3.951 3.060 0.789 -0.461 -1.230 - - - 146.121 -0.303 -0.514 Inflation 0.436 1.607 1.038 0.373 0.201 -0.209 ROA (in %) 0.170 0.630 0.376 0.089 0.377 1.900 ROE (in %) 4.100 10.610 7.276 1.462 0.259 0.164 Unemployment 2.400 5.100 3.691 0.835 0.113 -0.958 Interest rate -0.982 3.561 1.371 1.461 -0.100 -0.861 Exchange rate 69.417 101.139 83.660 12.346 0.578 -1.529 - - - 606.183 0.525 -1.033 -1.895 2.145 -0.092 1.306 0.409 -0.709 ROA (in %) 0.100 0.460 0.349 0.119 -1.227 1.208 ROE (in %) 1.810 12.520 7.289 2.741 -0.181 3.276 Unemployment 3.830 7.416 5.777 1.226 -0.029 -1.106 Interest rate 0.176 1.803 0.498 0.526 2.361 5.727 95.589 100.236 98.373 1.729 -0.479 -1.590 765.265 914.105 850.476 51.756 -0.497 -0.811 Inflation 0.194 2.208 0.979 0.648 0.584 0.101 ROA (in %) 0.170 0.660 0.439 0.128 -0.659 2.998 ROE (in %) 2.650 10.580 6.302 2.036 0.551 3.428 15.255 26.094 21.194 3.597 -0.274 -0.800 93.697 100.400 97.577 2.523 -0.518 -1.388 - - - 91.228 -0.350 -0.490 Inflation -0.223 1.381 0.393 0.543 0.865 -0.148 ROA (in %) -0.140 1.050 0.223 0.305 0.968 0.334 ROE (in %) -2.900 17.100 3.588 5.083 0.901 0.220 1.172 2.382 1.461 0.405 1.500 0.890 -1.509 -1.018 -1.284 0.144 0.377 -0.456 0.608 0.777 0.675 0.060 0.674 -1.288 - - - 166.030 0.233 -0.277 0.581 2.140 1.745 0.462 -1.805 2.640 ROA (in %) -0.430 1.420 0.670 0.414 -0.365 -0.063 ROE (in %) -3.610 12.530 7.270 3.719 -1.007 0.893 Unemployment 3.896 9.633 6.510 1.985 0.231 -1.415 Interest rate 1.137 2.486 1.834 0.494 -0.126 -1.695 Exchange rate 1.000 1.000 1.000 0.000 - - - - 0.179 -1.077 1.069 2.360 1.694 0.448 -0.293 -1.317 Interest rate Exchange rate GDP Inflation Italy Exchange rate GDP Japan GDP Inflation Netherlands Exchange rate GDP Unemployment Spain Interest rate Exchange rate GDP Unemployment UK Interest rate Exchange rate GDP Inflation USA GDP Inflation Table 1 represented the country wise descriptive statistics comprising of minimum value, maximum value, mean, standard deviation, skewness, and kurtosis of the variables under study. Skewness is a measure of the asymmetry of the probability distribution of a random variable about its mean. kurtosis identifies whether the tails of a given distribution contain extreme values. Some says for skewness (−1,1) and (−2,2) for kurtosis is an acceptable range for being normally distributed. If skewness is less than −1 or greater than +1, the distribution is highly skewed. These two measures are used to see the normality of the data. From the table above it can be seen that our almost all data is normally distribute. Curriculum Vitae along with Portfolio: Khalil Ahmad 4 Figure 1. Time series graphs of comparing the trend of mean of ROE (in %) From figure 1 it is cleared that the China has highest ROA (in %) profitability form 2010 to 2017, after 2017 The Canada took this place but both the China and the Canada have greater profitablity than rest of the countries. The China attained the highest value in 2011 and have downward trend form 2011 upto 2016 and again had increased the profitablity in 2017. The Italy got the minimum profit in 2011 and increased the profitabilty in 2012, again lose in from 2012 to 2014 then improved its profitabiltiy onward. The Germany got its maximum profitability in 2012 and minimum in 2015. It is cleared that the Germany is the country with minimum profitablity. Figure 2. Time series graphs of comparing the trend of mean of ROA (in %) Figure 3. Time series graphs of comparing the trend of mean of unemployment Research Hypotheses Hypothesis that I have developed is based on these five variables are: Null hypothesis-I: H0 = There is no relationship between working ROA (in %) and independent variables: unemployment, interest rate, .exchange rate, GDP, inflation Alternative hypothesis H1 = There is indirect relationship between unemployment and ROA (in %). H2 = There is direct relationship between interest rate and ROA (in %). H3 = There is indirect relationship between exchange rate and ROA (in %). H4 = There is direct relationship between GDP and ROA (in %) H5 = There is indirect relationship between inflation and ROA (in %). Curriculum Vitae along with Portfolio: Khalil Ahmad 5 Correlation Analysis Table 3. Correlation Analysis of ROA (in %) with other Independent variables Correlations Variables ROA (in %) Interest rate Exchange rate GDP 1 ROA (in %) Unemployment Unemployment -0.171** 1 0.009 Interest rate Exchange rate GDP Inflation 0.258** 0.383** 0.000 0.000 ** 0.366** 0.011 0.000 0.000 0.888 ** ** 0.370** -.638** 0.000 0.005 0.000 0.000 ** ** ** -0.408** 0.169** 0.000 0.000 0.010 -0.332 0.397 -0.438 -0.185 -0.230 - **. Correlation is significant at the 0.01 level (2-tailed). 1 -.499 1 1 Table 3 provided the degree of relationship between all variables under studies. The significant positive sign of the correlation coefficient represents direct relationship between indicators while the significant negative sign is for indirect relationship. The correlation coefficient of ROA (in %) and unemployment is -0.171, highly statistically significant as the p-value is < 0.01, its negative sign ensured that there is indirect relationship between ROA (in %) and unemployment. The correlation coefficient of ROA (in %) and interest rate is 0.258, highly statistically significant as the p-value is < 0.01, its positive sign ensured that there is direct relationship between ROA (in %) and interest rate. The correlation coefficient of ROA (in %) and exchange rate is -0.332, highly statistically significant as the p-value is < 0.01, its negative sign ensured that there is indirect relationship between ROA (in %) and exchange rate. The correlation coefficient of ROA (in %) and GDP is 0.397, highly statistically significant as the p-value is < 0.01, its positive sign ensured that there is direct relationship between ROA (in %) and GDP. The correlation coefficient of ROA (in %) and inflation is -0.438, highly statistically significant as the pvalue is < 0.01, its negative sign ensured that there is indirect relationship between ROA (in %) and inflation. Regression Analysis of ROA (in %) with other independent variables Table 5. Variance Inflation factor for Multicollinearity VIF 1/VIF GDP 3.411 .293 Interest Rate 2.265 .441 Inflation 1.808 .553 Unemployment 1.596 .627 Exchange Rate 1.185 .844 Mean VIF 2.053 . There is no multicollinearity between the variables. Table 6. Breusch-Pagan / Cook-Weisberg test for heteroskedasticity Source chi2 df Heteroskedasticity- Skewness 1.470 5 Kurtosis 2.920 1 Total- p- Breusch-Pagan / Cook-Weisberg test for heteroskedasticity Ho: Constant variance Variables: fitted values of ROA (in%) chi2(1) = 3.04 Prob > chi2 = 0.0810 The Breusch-Pagan / Cook-Weisberg test for heteroskedasticity suggested that there is no heteroskedasticity as p-value = 0.0810 > 0.05. Curriculum Vitae along with Portfolio: Khalil Ahmad Table 7. Normal Probability Plots of the variables under study Normality Plots of the Variable under study Table 7 showed that the data on all variables is approximately normally distributed. 6 Curriculum Vitae along with Portfolio: Khalil Ahmad 7 Regression Analysis The model that I have decided to use for analysis of panel data is (ROA(in %))it = 0 + 1(Unemployment)it + 2 (Interest rate)it + 3 (Exchagerate)it + 4 (GDP)it + 5 (Inflation)it +  it i=1, 2,3,..., N; t = 1, 2,3,...,T; The subscript i in the model is a cross-sectional unit such as a company and t represents the time dimension. Where (ROA(in%)) is our dependent variable, following are independent variables (Unemployment), (Interest rate), (Exchange rate), (GDP), (Inflation), and  it is the error term. Empirical Regression Modeling Empirical model is developed to analyze the impact of working capital management on profitability of the selected companies. For this purpose, panel data of 10 countries and 26 banks recorded from 2010 to 2018 are used to develop this model empirically. After implementation of full regression model, we obtained the following empirical models. Empirical Regression Model of ROA (in %) (ROA(in %))it = 0.366 − 0.012(Unemployment)it + 0.1345(Interest rate)it − 0.0006(Exchagerate)it -(GDP)it − 0.134(Inflation)it + it i=1, 2,3,..., N; t = 1, 2,3,...,T; Table 8. Normal Probability Plots of the variables under study ROA (in%) Coef. St.Err. t-value p-value [95% Conf Interval] Sig Unemployment - - -- Interest Rate- - *** Exchange Rate -- - -- GDP 1.72e-6 7.71e- - Inflation - -- *** Constant- *** Mean dependent var Overall r-squared Chi-square R-squared within *** p<.01, ** p<.05, * p<.1 - SD dependent var Number of obs Prob > chi2 R-squared between - The above table showed that the proposed model is highly significant as the p-value of F-test is 0.000 <0.01, 1% level of significance. It explained the overall 68.6% variation as the R-square value is presented there. The empirically estimated parameters of the proposed model are presented as coefficients in the second column of the table 8 which showed that if one unit of unemployment is increased keeping the effect of other as constant then there will be on average 0.0125 unit decrease in ROA (in %). If one unit of interest rate is increased keeping the effect of other as constant, then there will be on average 0.1345 unit increase in ROA (in %), the coefficient of the interest rate is highly significant as p-value is 0.000 < 0.01. Other results can be interpreted in the similar way. Project-III: Time Series Analysis Time Series Forecasting using different Approaches with R Curriculum Vitae along with Portfolio: Khalil Ahmad 8 Table 4.1 Candidate SARIMA Models Model AIC Model AIC ARIMA(0,1,0)(0,1,0) - ARIMA(1,1,4)(0,1,0) - ARIMA(0,1,1)(0,1,0) - ARIMA(2,1,0)(0,1,0) - ARIMA(0,1,2)(0,1,0) - ARIMA(2,1,1)(0,1,0) - ARIMA(0,1,3)(0,1,0) - ARIMA(3,1,0)(0,1,0) - ARIMA(0,1,4)(0,1,0) - ARIMA(3,1,1)(0,1,0) - ARIMA(0,1,5)(0,1,0) - ARIMA(4,1,0)(0,1,0) - ARIMA(1,1,0)(0,1,0) - ARIMA(4,1,1)(0,1,0) - ARIMA(1,1,1)(0,1,0) - ARIMA(5,1,0)(0,1,0) - Table 4.10 Mean Square Error of Artificial Neural Network Method MSE ANN fit with (10,5) hidden nodes 3.4394 Curriculum Vitae along with Portfolio: Khalil Ahmad Figure 4.10:- Graphical presentation of Artificial Neural Network Figure 4.16:- Graph of Forecast using Artificial Neural Network Forecasting using Non-parametric Technique 4.2 9 Curriculum Vitae along with Portfolio: Khalil Ahmad 10 (a) (b) (c) (d) Table 5.1 Conclusions and Recommendations Forecasting Methods RMSE SARIMA Model 10.8925 Bayesian Approach - Non-parametric Method KNN - ANN with 5 Hidden nodes 11.0876 ANN fit with (10,5) hidden nodes 3.4394