I attached the project information
· collect financial or economic time series data and conduct forecasting using simple exponential smoothing, time series decomposition and time series regression techniques. · Use any other source to collect financial data, either company’s stock daily close price, or monthly financial index such TSX and SP500, or Price Index by industry; · You need to collect the most recent observation for at least 500 observations. You need to save the data into a data file in which two columns of data are created, i.e., time and observed values. Your tasks a) Provide a short description of your data, make a proposal on how you can use this data to forecast future values, and discuss the necessary assumption you made in order to conduct meaningful forecasting. b) Plot the time series and plot the autocorrelation function using R. If the time series appear to be non-stationary, then also plot the autocorrelation function for the first- order difference of the original time series. (c) Comment on the data characteristics based on the results you got from the time series plot and ACF plots. d) Using a simple exponential smoothing technique, do the forecast for the next period and plot the original data and their forecast values in the same figure. Evaluate the accuracy of the exponential smoothing techniques. You must determine the optimal smoothing constant ? by evaluating the forecast error using different values of α. You can just try ? =0.1, 0.2, ..., 0.9. The process must be done using excel. Note that, within this step, you must clearly state the initial value for the simple exponential smoothing. e) Compare the optimal ? value from the analysis using excel to the value that was automatically selected by R. Do you observe some kinds of consistency? Explain why or why not? f) Run the following auto-regression by fitting the model to the data that you collected. Yt =b +bYt-1+bYt-2+et 012 Note that the above regression model assumes that you have stationary time series. If your time series is non-stationary, you must do differencing on it to achieve a stationary time series so that the regression can be done appropriately. g) Validate the model by checking the assumptions of the time series regression model above. h) Does the residual variance appear to be constant? Using the box-cox transformation to determine the optimal lambda to transform ? and re-run the regression model using the transformed data. (Note that, in the regression analysis, the lagged values must be constructed from the transformed series, not the original ? .) i) Comment on the differences in the residual pattern in terms of homogeneity of residual variance before and after the box-cox transformation. j) Forecast the value of ? for each time period, using the regression model for both with ? and without the box-cox transformation, and compare the results to the one that uses the simple exponential smoothing method. Which forecast method works best for the data? Report their accuracy measures (using the R function to produce the accuracy measures.) Justify your answer. (Note that you are comparing three forecast methods.) k) Apply the ARIMA modelling technique to come up with the ARIMA model. Report the p, d, q parameters and the associated standard deviations of the model coefficient estimates. Make sure that you apply ARIMA to the original time series data. Please note that the report must cover all items mentioned above; if there are some items that you did not complete, make sure that you highlight them and describe the reasons why they are not completed. Failure to do this will significantly affect the overall mark for this project.