1 / 26

Seasonal Forecast Models for Price Analysis

Learn how to incorporate seasonal differences in prices to forecast monthly prices using seasonal and moving average forecast models. Explore seasonal indices, composite forecast models, dummy variable regression models, and harmonic regression models.

jshirey
Download Presentation

Seasonal Forecast Models for Price Analysis

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lecture 9 Seasonal Models • Materials for this lecture • Lecture 9Seasonal Analysis.XLSX • Read Chapter 15 pages 8-18 • Read Chapter 16 Section 14

  2. Uses for Seasonal Models • Have you noticed a difference in prices from one season to another? • Tomatoes, avocados, grapes, lettuce • Wheat, corn, hay • 450-550 pound Steers • Gasoline • You must explicitly incorporate the seasonal differences of prices to be able to forecast monthly prices

  3. Seasonal and Moving Average Forecasts • Monthly, weekly and quarterly data generally have a seasonal pattern • Seasonal patterns repeat each year, as: • Seasonal production due to climate or weather (seasons of the year or rainfall/drought) • Seasonal demand (holidays, summer) • Cycle may also be present and the seasonal pattern is mapped over the top of the cycle Lecture 3

  4. Econometric Seasonal Forecast Models • Seasonal indices • Composite forecast models • Dummy variable regression model • Harmonic regression model • Moving average model

  5. Seasonal Forecast Model Development • Steps to follow for Seasonal Index model development • Graph the data • Check for a trend and seasonal pattern • Develop and use a seasonal index if no trend is present • If a trend is present, forecast the trend and combine it with a seasonal index • Develop the composite forecast • Trend and seasonal components

  6. Two kinds of Seasonal Indices • Price Index • The traditional index value shows the relative relationship of price between months or quarters • It is ONLY used with price data • Fractional Contribution Index • If the variable is a quantity we calculate a fractional contribution index to show the relative contribution of each month to the annual total quantity • It is ONLY used with quantities

  7. Seasonal Index Model • Seasonal index is a simple way to forecast a monthly or quarterly data series • Index represents the fraction that each month’s price or sales is above or below the annual mean • Steps to calculate a seasonal index

  8. Using a Seasonal Price Index for Forecasting • Seasonal index has an average of 1.0 • Each month’s seasonal index value is a fraction of the annual mean price • Use a trend or structural model to forecast the annual mean price • Use seasonal index to deterministiclyforecast monthly prices from annual average price forecast PJan = Annual Avg Price * IndexJan PMar = Annual Avg Price * IndexMar • For an annual average price of $125 Jan Price = 125 * 0.600 = 75.0 Mar Price = 125 * 0.976 = 122.0

  9. Seasonal Index Model

  10. Using a Fractional Contribution Index • Fractional Contribution Index sums to 1.0 to represent annual quantity (e.g. sales) • Each month’s value is the fraction of total sales in the particular month • Use a trend or structural model for the deterministic forecast of annual sales SalesJan= Total Annual Sales * IndexJan SalesJun= Total Annual Sales * IndexJun • For an annual sales forecast at 340,000 units SalesJan= 340,000 * 0.050 = 17,000.0 SalesJun= 340,000 * 0.076 = 25,840.0 • This forecast is useful for planning production, input procurement, and inventory management • The forecast can be probabilistic

  11. OLS Seasonal Forecast with Dummy Variable Models • Dummy variable regression model can account for trend and season • Include a trend if one is present • Regression model to be estimated is: Ŷ = a + b1Jan + b2Feb + … + b11Nov + b13T • Jan – Nov are individual dummy variable 0’s and 1’s • Effect of Dec is captured in the intercept • If the data are quarterly, use 3 dummy variables, for first 3 quarters and intercept picks up affect for fourth quarter Ŷ = a + b1Qt1 + b2Qt2 + b11Qt3 + b13T

  12. Seasonal Forecast with Dummy Variable Models • Set up X matrix with 0’s and 1’s • Easy to forecast as the seasonal effect is assumed to persist forever • Note the pattern of 0s and 1s for months • December affect is captured in the intercept

  13. Seasonal Forecast with Dummy Variable Models • Regression Results for Monthly Dummy Variable Model • May not have significant effect for each month • Must include all months when using model to forecast • Jan forecast = 45.93+4.147 * (1) +1.553*T -0.017 *T2+0.0001 * T3

  14. Probabilistic MonthlyForecasts

  15. Probabilistic MonthlyForecasts • Use the stochastic Indices to simulate stochastic monthly forecasts

  16. Probabilistic Forecast with Dummy Variable Models • Stochastic simulation to develop a probabilistic forecast of a random variable Ỹij= NORM(Ŷij, σ)

  17. Harmonic Regression for Seasonal Models • Sin and Cos functions in OLS regression used to isolate seasonal variation • Define a variable SL to represent alternative seasonal lengths: 2, 3, 4, … • Create the X Matrix for OLS regression X1 =Trend so it is: T = 1, 2, 3, 4, 5, … . X2 =Sin(2 * ρi() * T / SL) X3 =Cos(2 * ρi() * T / SL) Fit the regression equation of: Ŷi = a + b1T + b2 Sin((2 * ρi() * T) / SL) + b3 Cos((2 * ρi() * T) / SL) + b4T2+ b5T3 • Only include T if a trend is present

  18. Harmonic Regression for Seasonal Models This is what the X matrix looks like for a Harmonic Regression

  19. Harmonic Regression for Seasonal Models

  20. Moving Average Forecasts • Moving average forecasts are used by the industry as the naive forecast • If you can not beat the MA then you can be replaced by a simple forecast methodology • Calculate a MA of length K periods and move the average each period, drop the oldest and add the newest value 3 Period MA Ŷ4= (Y1 + Y2 + Y3) / 3 Ŷ5= (Y2 + Y3 + Y4) / 3 Ŷ6= (Y3 + Y4 + Y5) / 3

  21. Moving Average Forecasts • Example of a 12 Month MA model estimated and forecasted with Simetar • Change slide scale to experiment MA length • MA with lowest MAPE is best but still leave a couple of periods

  22. Probabilistic Moving Average Forecasts • Use the MA model with lowest MAPE but with a reasonable number of periods • Simulate the forecasted values as Ỹi = NORM(Ŷi, σ ) Simetar does a static Ŷiprobabilistic forecast • Caution on simulating to many periods with a static probabilistic forecast ỸT+5 = N((YT+1 +YT+2 + YT+3 + YT+4)/4), σ ) • For a dynamic simulation forecast ỸT+5= N((ỸT+1+ỸT+2+ ỸT+3+ ỸT+4)/4, σ )

  23. Moving Average Forecasts

  24. Probabilistic Forecast for Seasonal Models • Stochastic simulation used to develop a probabilistic forecast for a random variable Ỹi = NORM(Ŷi , σ) Ŷi is the forecast for each future period based on your expectations of the exogenous variables for future periods σ is a constant and is calculated as the stddev of the residuals

More Related