Forecasting with Time Series Types of Data o Cross sectional data data collected at the same or approximately the same point in time often for multiple variables o Time series data data collected at more than one period of time sequentially over several periods at regular intervals for one variable Na ve Forecasting Methods o One Period Lag o K Period Moving Average Self explanatory simply move the actual from period before to the forecast of current period Self explanatory take the number of periods from k and average the actual from periods and use average as forecast for current period o K Period Weighted Moving Average Assign weights to the k most recent observations The weights are chosen by the user and usually assign increasing weight to more recent observations Total weight actual and divide by total weight Evaluating Accuracy of the Forecasting Method o Forecast Error Otherwise known as observed expected Forecast error for a given time period t et yt yt o Forecast Accuracy Measures Mean Square Error Mean Absolute Deviation Mean Absolute Percentage Error Less than 8 signifies a good model In all three measures n is the number of errors used to obtain the numerator The MSE and MAD are units affected while MAPE is not This allows us to attach a rule of thumb to the use of MAPE A forecasting method is generally considered effective if the MAPE is 8 Exponential Smoothing o Simple Exponential Smoothing A type of weighted average that includes all previous observations in the time series A weighted average of the most recent observation in the time series yt 1 and the forecast of that observation yt 1 w yt 1 1 w yt 1 w called omega is the smoothing constant 0 w 1 w above 0 5 Forecast for week 1 and week 2 will always be the same focus on most current observation w below 0 5 w o Time Series with components focus on the history Trend Component Persistent overall upward or downward pattern in the response variable over many periods Contributors include changes in size and geographic distribution of population technological improvements gradual shifts in habits Cyclical Component Measured in years Shifts in the direction of the response variable from time to time with varying intensity and duration We tend to view these as expansion or contraction periods in the economy lasting 2 to several years Contributors include buildups and depletions of inventories shifts in rates of capital investments changes in governmental monetary policies weather patterns wars etc Seasonal Components Regular and repeating pattern of fluctuations Due to weather customs etc Completes itself within 1 year Irregular Component Erratic unsystematic fluctuations Due to random variation or unforeseen events o Union Strike o Tornado Short duration nonrepeating o Smoothing Reduce Random Component Smoothing techniques If we can determine which components actually exist in a time series we can develop better forecasts We can reduce random variation by smoothing the time series Methods to smooth the data are o Moving averages Used to look at trends not forecast Centered moving average With an even number of observation included in the moving average the average is placed between the two period in the middle To place the moving average in an actual time period we need to center it Two consecutive moving averages are centered by taking their average and placing it in the middle between them o Exponential smoothing There are two drawbacks with the moving average method of smoothing No moving averages for the first and last sets of time periods The moving average forgets most of the previous time series values i e only looks at those around it Exponential smoothing addresses these issues Use as for forecasting