ECON 325 -- Forecasting

1. ECON 325 -- Forecasting Preliminaries & Introduction

2. Course Assumptions • This is not an introduction to R, per se, but as part of the course we will be spending a significant time using the R software platform. • R is integrated into the text that we’ll be using, and your homework assignments will typically utilize R. To some degree, however, it’s YOUR responsibility to learn the software. • Some concepts will also be illustrated in Excel, so that you can see how they work, rather than simply the end product.

3. Course Assumptions • This is most definitely not a statistics course. I assume you are familiar with concepts such as: • Mean • Standard deviation • Probability distributions (e.g., normal distribution) • Quantiles, etc. • While previous experience with cross-sectional regression is recommended, it isn’t required.

4. Course Assumptions • This is also not a theory course. There won’t be any proofs or derivations. My goal is to teach you forecasting tools, as well as instruct you when and how to use them most effectively.

5. What can be forecast? • Pretty much anything where past patterns can be expected to evolve in the same manner into the future.

6. What can be forecast? Some of the areas in which forecasting currently plays an important role are: • Scheduling: Forecasts of the level of demand for product, material, labor, financing, or service are an essential input to scheduling. • Acquiring resources: Forecasting is required to determine future resource requirements. • Determining resource requirements: All organizations must determine what resources they want to have in the long-term. These determinations all require good forecasts and managers who can interpret the predictions and make appropriate decisions.

7. What can be forecast? • The environment doesn’t have to be static. Rather, the environment must be expected to change in a predictable manner.

8. What can be forecast? • There’s a difference between forecast accuracy and precision in identifying a particular variable’s law of motion. • Example: exchange rates follow a random walk over the short run

9. Overview of forecasting techniques • Forecasting situations vary widely in their time horizons, types of data patterns, factors affecting actual outcomes, and many other aspects.

10. Qualitative forecasting • If there are no data available, or if the data available are not relevant to the forecasts, then qualitative forecasting methods must be used. These methods are not purely guesswork – there are well-developed approaches for getting good forecasts without using historical data.

11. Quantitative forecasting • Can be applied when two conditions are satisfied: • Numerical information about the past is available • It is reasonable to assume that some aspects of the past patterns will continue into the future. • Continuity assumption • Wide range of quantitative forecasting methods: time series methods (data collected at regular intervals over time) or cross sectional data (data collected at a single point in time)

12. Unpredictable events • Little or no information is available. • Example: likely impact of Yellowstone super-volcano eruption is ???

13. Cross-sectional forecasting • We are wanting to predict the value of something we have not observed, using the information on the cases that we have observed. • Examples: • Hedonic pricing. Suppose you have data on housing prices for all houses sold in 2011 in a particular area, but are interested in predicting the price of a house not in our data set using various house characteristics (position, # of bedrooms, age, etc.) • Fuel economic data for a range of 2009 model cars. We are interested in predicting the carbon footprint of a vehicle not in our data set using information such as the size of the engine and the fuel efficiency of the car.

14. Cross-sectional forecasting • Cross-sectional models are used when the variable to be forecast exhibits a relationship with one or more other predictor variables. • The purpose of the cross-sectional model is to describe the form of the relationship and use it to forecasts values of the forecast variable that have not been observed. • Under this model, any change in predictors will affect the output of the system in a predictable way, assuming that the relationship does not change. • Models in this class include regression models, additive models, and some kinds of neural networks.

15. Car Emissions Example

16. Car Emissions Example • Table 1.1: Fuel economy and carbon footprints for 2009 model cars with automatic transmissions, four cylinders and small engines. City and Highway represent fuel economy while driving in the city and on the highway. • A forecaster may wish to predict the carbon footprint (tons of CO2 per year) for other similar vehicles that are not included in the above table.

17. Car Emissions Example • Forecasting Procedure: • It is necessary to first estimate the effects of the predictors (number of cylinders, size of engine, and fuel economy) on the variable to be forecast (carbon footprint). • Then, provided that we know the predictors for a car not in the table, we can forecast its carbon footprint.

18. Car Emissions Example R code for scatter plot and regression line: plot(jitter(Carbon) ~ jitter(City),xlab="City (mpg)",ylab="Carbon footprint (tons per year)",data=fuel)fit <- lm(Carbon ~ City, data=fuel)abline(fit) This scatter plot illustrates Carbon (carbon footprint in tonnes per year) versus City (fuel economy in city driving conditions in miles per gallon) for all 134 cars. Also plotted is the estimated regression line: .

19. Car Emissions Example • For a car with City driving fuel economy x=30 mpg, the average footprint forecasted is tons of CO2 per year. The corresponding 95% and 80% forecast intervals are [4.95,6.84] and [5.28,6.51] respectively (calculated using R). • R code for forecast value: fitted(fit)[1]fcast <- forecast(fit, newdata=data.frame(City=30))plot(fcast, xlab="City (mpg)", ylab="Carbon footprint (tons per year)")

20. Explanatory vs Time Series Forecasting There is an important distinction between explanatory (or causal) modelsand time series models. There is some semantic confusion with this choice of words because “explanatory models” can deal with “time series” data.

21. Time Series Models • When we say time series models or time series methods we usually mean to talk about one set of (time-dependent) data and we will try to develop a model (an equation) which can be thought of as the “generating process” of these data. • We specifically will not look at its relationship with other variables. That is, the system is treated as a black box and makes no attempt to discover the factors affecting its behavior.

22. Time Series Models There are two main reasons for wanting to treat a system as a black box. • The system may not be understood, and even if it were understood it may be extremely difficult to measure the relationships assumed to govern its behavior. • The main concern may be only to predict what will happen, and not to know why it happens.

23. Explanatory Models When we say causal models we are specifically looking for other variables (which may be time series) which offer explanations (or linkages) to the main variable (which may also be a time series). • Explanatory models assume that the variable to be forecasted exhibits an explanatory relationship with one or more independent variables. • The purpose of the explanatory model is to discover the form of the relationship and use it to forecast future values of the forecast variable.

24. Time Series vs. Explanatory Models Both time series and explanatory models have advantages in certain situations. • Time series models can often be used more easily to forecast • Explanatory models can be used with greater success for policy and decision making.

25. Exercise Several approaches have been suggested by those attempting to predict stock market movements. Three of them are described briefly below. How does each relate to the different approaches to forecasting described here? • A. Dow Theory: There tend to be support levels (lower bounds) and resistance levels (upper bounds) for stock prices both for the overall market and for individual stocks. These levels can be found by plotting prices of the market or stock over time. • B. Random Walk Theory: No way to predict future movements in the stock market or individual stocks, since all available info is quickly assimilated by the investors and moves market prices in the appropriate direction. • C. Prices of individual stocks or of the market in general are largely determined by earnings (e.g., dividend growth model).