Forecasting Techniques: Naïve Methods Su, Chapter 10, sections I-II

Forecasting Exercises: Data Table 10.2 in Su Annual New Car Sales (in thousands) and a New Automobile Price Index ( =100) for

Forecasting Exercises First, read the file table10-2.dat into excel –This file contains three columns, containing dates (Col. A), New Car Sales (Col. B) and the New Car Price Index (Col. C) Extend the date column through 1999 Label Columns D-H: No Change, Same Change, Same Ratio, MA, Partial Adjustment

No Change Model Simplest Naïve Model Often used without even realizing it Requires only one period of historical data Anticipated level of the variable this period is the same as last period X* t = X t-1 X* t : Forecast value

Same Change Model No change model in first differences  X* t =  X t-1 X* t - X t-1 = X t-1 - X t-2 Requires only 2 periods of past data

Same Ratio Model Same change model in multiplicative form (X* t / X t-1 ) = (X t-1 / X t-2 ) X* t = X t-1 (X t-1 /X t-2 )

Three Naïve Forecasts

Evaluating these Forecasts What are the underlying assumptions? How much historical data were used by each How accurate are they? Over how long a period should these forecasts be evaluated?

Defining and Measuring Accuracy Reading: Su, Chapter 16, section I-II The criteria that should be used to measure forecast accuracy are open to debate; we’ll look at the main competing methods Assessment of forecast accuracy is a very important component of forecast evaluation

Definitions: Forecast Errors Forecast Error in Levels FE t in level = F t - A t FE t : Forecasting Error in period t F t : Forecast in period t A t : Actual (or Realized) value in period t Forecast error measured in same units as variable FE t > 0 Overestimate FE t < 0 Underestimate

Summary Statistics Must avoid problems associated with signs of forecast errors - can’t simply add them up! Two ways to correct for this: –Absolute Value –Squaring

Three Summary Statistics Mean Absolute Error (MAE) MAE =  |FE t | / n =  |F t - A t | / n Mean Square error (MSE) MSE =  (FE t ) 2 / n =  (F t - A t ) 2 / n Root Mean Square Error (RMSE) RMSE = SQRT[  (FE t ) 2 / n =  (F t - A t ) 2 / n]

Naïve Forecasts: In-Sample Measurement of Accuracy Use these definitions to evaluate the accuracy of these three naïve methods We’ll use “In-Sample” evaluation, as we have a lot of historical data but require very little to make these forecasts Step 1: Copy Table to a new sheet Step 2: Calculate in-sample forecasts Step 3: Calculate forecast error Step 4: Calculate Summary Statistics

Summary Statistics No Change MAE = MSE = RMSE = Same Change MAE = MSE = RMSE = Same Ratio MAE = MSE = RMSE =

Conclusions From Summary Statistics Which is the “best” at one-period ahead forecasts?

Moving Average Methods Provides more efficient mechanical projections of short-term movements Has advantage of flexibility and presents a more realistic picture of long-run movements Data are not forced into any particular patterns MA: X* t = (1/n)  n i   X t-i =(1/n)[X t-1 +X t-2 + X t X t-n ] Note this is not a centered moving average Must only decide on n Can be applied to first differences or % changes

Moving Average Example Start with an MA(4) forecast –For ease of coding, copy the car sales values to the MA column, then the out of sample MA forecast can be easily written and copied Compute the within sample, one period ahead MAE, MSE, RMSE

Naïve Forecasts and MA(4)

Changing the Order of an MA Forecast Economists refer to MA forecasts by the number of periods they use, which is called the “order” of the moving average –MA(2): Two period moving average –MA(3): Three period moving average –etc. The forecast depends on the MA order

Effect of Changing Order