Forecasting Coursework Introduction The data of this coursework are business Investment In the quarterly series In the manufacturing sector from 1 994 to the second quarter of 2008 In ASK. In the coursework, firstly analyze the former 50 data to forecast the latter 8 ones and then compare with the real data to see if the forecasting model Is a good fit or not.
As adopting two different approaches to make the forecasting work, including regression with Dummy Variables method and Box-Jenkins IRMA method, according to the results, relative comparisons will be made to demonstrate which one is a better hooch for this certain question. Then discuss the underlying assumptions of the chosen model and evaluate whether it is sensitive to these assumptions. All the analyses are based on the SPAS software and the graphs are from the output. Part 1.
Examine the data To apply certain model to forecast future value, find out the seasonal component, trends and cycles component is the basic Job. There are two approaches to examine the data: see the time series plot (chart 1) or use GAFF (chart 2). Chart 1 Plot of the data Chart 2 GAFF/PACE of the data From both Chart 1 and Chart 2, the drawing conclusion is that the data has trend- yes and seasonal components. Firstly, although there is no general upward trend and downward trend, clearly there is a cycle component: the data value climbs up in the first 20 data and then displays a down trend following behind.
As to seasonal component, It Is clearly from the time series plot that In each year the highest Investment happened In the fourth quarter, while the lowest one occurred around the first quarter. From the GAFF plot, the most significant autocorrelation Is In lag 4, and there is also a spike in lag 8, indicating that there is a quarterly seasonal component. By carrying out a first difference, the GAFF series plot display obvious quarterly seasonal component. Therefore the data value has a cycle component and a quarterly seasonal component.
Part 2. Dummy variable model According to the analysis in Part 1, there is a seasonal effect in investment, specifically quarterly Influence. Therefore, four dummy variables, including IQ , SQ, SQ and SQ are made for this method, although SQ will not be used in the process. As there are linear and nonlinear trend-cycle model, this report will take all three ones Into consideration: linear trend-cycle, quadratic trend-cycle and cubic trend-cycle del. As it is a linear trend-cycle and seasonal model, a new variable TIME is created.
Due to multi-collinear, there is no need to include all four dummy variables, Just three is enough. Hence, the equation of this multiple regression with dummy variables model is: Forecasting Then do regression process in SPAS, the output is displaying as follows. I Model Summary I lb. Dependent Variable: investment I Coefficients Model I I Model Because all the regression coefficients are significant at 5% level, there is no need to take any variables out of the equation. As a result the forecasting equation is: Forecasting IQ -922. 1 [pet]TPTB] From the Adjusted R square value, the plot of real value and forecasting value, the plot of error and also the GAFF chart of Unanswered Residual, the conclusion is that this model is not a good one. The Adjusted R Square is 0. 392, at a low level. It is clear from the time series plot that the model do not fit the modeling data value well, although there are some time point the gap between the predict value and real value are quite small. However, for the halfback data, the model seems to have a good fit as drawn from the chart. It shares the same curve trend with raw data and has a small fluctuation.
As for error component, it has a mean of 6, quite near to zero and this shows the overall predict result acceptable. And the GAFF plot of the residual shows quite a few significant autocorrelations from lag 1 to lag 6, while the PACE plot has significance in lag 1 . All these indicate that this model is not very good and it can be enhanced by some ways. 2. Quadratic trend-cycle *seasonal model In this model a new dummy variable of TIME=Tale*Tale is introduced in. And the equation is: Forecasting value=a+CLC *IQ +be*SQ+be*SQ+error Output are displaying as follows.
I I Model Summary Dependent Variable: investment Coefficients Because all regression coefficients are significant at 5% level, no dummy variable need to be taken out. Thus, the final quadratic trend-cycle *seasonal model equation is: Forecasting value = 4503. 761 [pet]TPTB] but no good enough as well. Firstly, the Adjust R Square is 0. 711 and this is a good fit. Secondly, the plot of predicted value and raw data fit quite well in several years of modeling data, such as year 2001. However the result of the halfback data is not good, actually forecasting data shows an opposite trend to real one.
