LINKÖPINGS UNIVERSITET732G06 TIME SERIES ANALYSIS
Institutionen för datavetenskapFall semester 2008
Statistik, CL, ANdAssignment
Assignment week 38:
Solutions should be submitted by the end of week 39
Exponential smoothing of monthly observations of the General Index of the Stockholm Stock Exchange.
Data: Stock_Exchange.txt (download from web-site)
A. Graphical illustration of data
First, construct a graph of the original series of monthly values. Then construct a graph of the percentage change from month to month. Which smoothing techniques (single, double, Holt-Winters) can be used on the original series, which can be used on the series of percentage change.
B. Exponential smoothing with predefined smoothing parameters
Perform single exponential smoothing on the time series of percentage change (of the General Indices). Set the smoothing parameter, , first to 0.9 and then to 0.1. Then study the graphs produced and try to understand how the choice of the smoothing parameter affects the forecasted values.
C. Exponential smoothing with automatic parameter setting
Let the program choose an optimal value of the smoothing parameter and calculate forecasts for a two-year period (24 months) after the last observed time-point. Construct a graph for the errors in the one-step-ahead forecasts (residuals) in the whole time series and try to judge upon whether the forecasting methods uses earlier observations in the series in an efficient way. Are the residuals serially correlated – Make a visual judgement. Use also the autocorrelation function on the residual. (MINITAB-Time Series- Autocorrelation). What do you see in the plot you get?
Hints:
Exponential Smoothing in MINITAB:
Use the function: Single exponential, Double Exponential and Holt-Winters under 'Time Series'. These methods cannot deal with missing values. In the series of percentage change remove the first (missing) observation before the analysis.
.
Exponential smoothing of time series with seasonal variation
Data: Labourforce.txt (download from web-site)
A. Forecasting the employment in USA
Perform an exponential smoothing of the time series of monthly employments figures in USA and calculate forecasts for a two-year period (24month) after the last observed time-point. Then use a suitable model for time series decomposition to make forecasts for the same period (additive or multiplicative). Print out graphs for observed and forecasted values and compare how the seasonal effects are described in each method of forecasting. Which method do you prefer in this case?
B. Forecasting of monthly mean temperature
Data: temperature.txt (download from web-site)
Use exponential smoothing to make forecasts of monthly mean temperatures in Stockholm. Try single, double (Holt’s method) and Winters’ method.
Study the residuals (the errors in one-step-ahead forecasts) and the forecasts for 24 months after the last observed time-point. Are the one-month-ahead and one-year-ahead forecasts realistic?
Is there a better way for making forecasts than applying exponential smoothing on the original series?