Exam 23: Time-Series Analysis and Forecasting

The actual and forecast values of a time series are shown below. Actual values Forecast values 2325 2330 2555 2595 2835 2860 3185 3125 3510 3390 a. Calculate the mean absolute deviation (MAD). b. Calculate the sum of squares for forecast error (SSE).

The daily sales figures below have been recorded in a medium-sized insurance company. $\quad\quad\quad\quad\quad\quad\quad\quad\text { Week }$ Day 1 2 3 4 Monday 38 46 35 59 Tuesday 40 36 52 53 Wednesday 17 32 25 28 Thursday 20 17 28 33 Friday 26 20 32 20 a. Compute the three-day and five-day moving averages. b. Plot the series and the moving averages on the same graph. c. Does there appear to be a seasonal (weekly) pattern?

If data for a time-series analysis are collected on a monthly basis only, which component of the time series may be ignored?

Two forecasting models were used to predict the future values of a time series. These are shown in the following table, together with the actual values. $\text { Forecast Value } F_{t}$$\quad\quad\quad\text { Actual Value } y_{t}$ Model 1 Model 2 8.2 7.7 7.6 7.8 8.5 8.2 7.0 8.5 7.6 9.6 9.0 10.3 Compute MAD and SSE for each model to determine which was more accurate.

The following trend line and seasonal indexes were computed from five years of quarterly observations: $=1800+75 t-2 t^{2}$ . Quarter S 1 0.575 2 0.825 3 1.225 4 1.375 Forecast the four quarterly values for next year.

The equation F_t+1 = wy_t + (1-w)S_t-1 (for t $\ge$ 2) refers to a time series forecast prepared by exponential smoothing.