1. Data Sources
The most sophisticated forecasting model will fail if it is applied to unreliable data
Data should be reliable and accurate
Data should be relevant
Data should be consistent
Data should be timely

2. Forecasting Technique
Qualitative Forecasting - rely on judgment and intuition - scenario analysis, focus groups, some areas of market research
Quantitative Forecasting - used when historical data is available and the data is judged to be representative of the unknown future.
Statistical techniques - patterns, changes, and fluctuations - decompose data into trends, cycles, seasonality, random
Econometric & Box-Jenkins - do not assume that data are represented by separate components.
Deterministic or causal - identification of relationships (regression)

3. Types of Data
Cross-sectional: collected at a single point in time – all observations are from the same time period
Time Series – data that are collected, recorded or observed over successive increments of time

4. Time Series Components
Trend, cyclical, seasonal, random (review Introduction to Forecasting notes for descriptions)
When a variable is measured over time, observations in different time periods are frequently related or correlated.
Autocorrelation - correlation between a variable, lagged one or more periods, and itself. Used to identify time series data patterns.

5. Autocorrelation
Correlation measures the degree of dependence (or association) between two variables.
Autocorrelation means that the value of a series in one time period is related to the value of itself in previous periods. There is an automatic correlation between the observations in a series. For example, if there is a high positive autocorrelation, the value in June is positively related to the value in May.

6. Autocorrelation...
Random data? Is there a trend? Stationary data? Seasonal data?
If the series is random, the autocorrelation is close to 0 and the successive values are not related to one another
If the series has a trend, the data and one lag are highly correlated and the correlation coefficients are significantly different from zero and then drop toward zero.
Seasonality - significant autocorrelation occurs at the appropriate time lag: 4 for quarterly, 12 for monthly

7. 95% confidence interval - if autocorrelation is outside the range, have significance
Ho: r = 0
HA: r 0
Compare T to t-value: 2 tail test, 95% level of significance and n-1 d.f. t-value = 2.2
Reject Ho if T is less than -2.2 or if T is greater than 2.2
Conclusion:
Do Not Reject Ho:.
The autocorrelation is not
significantly different from zero
The series is random.

8. Autocorrelation Analysis
Autocorrelation coefficients of random data have a sampling distribution with a mean of zero and a standard deviation of 1/sqrt(n).
We test to see our data’s autocorrelation coefficients come from a population with the same distribution. If our sample is random, we expect the mean to equal zero.
We use the confidence interval to determine if our autocorrelation coefficients are within a certain range of zero, based on the standard deviation

9. Autocorrelation Analysis
If the series has a trend, the data is non-stationary. Advanced forecasting models require stationary data - average values do not change over time.
Autocorrelation coefficients drop to zero after the second time lag in stationary data.
Can remove a trend from a series by differencing (subtract the lagged data from original data) and check the correlogram to make sure the data does not show a trend.

10. Choosing a Forecasting Technique
Stationary data
Can transform stationary data - square roots, logs, differences
Forecasting errors can be used in simple models
Adjusting data for factors such as population growth
Simple models: averaging, simple exponential smoothing, naive

11. Choosing a Forecasting Technique
Forecasting Trends
Growth or decline over extended time-period
Increased productivity / changes in technology / population / purchasing power
Models: linear moving average, exponential smoothing, regression, growth curves

12. Choosing a Forecasting Technique
Forecasting Seasonality
Repeated pattern year after year
Multiplicative or additive method and estimating seasonal indexes
Weather or calendar influences
Models: classical decomposition, multiple regression, time series & Box-Jenkins

13. Other factors to consider
Selection depends on many factors - content and context of the forecast, availability of historical data, degree of accuracy desired, time periods to be forecast, cost/benefit to the company, time & resources available.
How far in the future are you forecasting? Ease of understanding. How does it compare to other models?
See Table in Text
Forecasts are usually incorrect (adjust)
Forecasts should be stated in intervals (estimate of accuracy)
Forecasts are more accurate for aggregate items
Forecasts are less accurate further into the future

14. Forecasting Error Some symbols: Y Actual Value Y ^ Forecasted Value Yt
Forecasted Value for time period t
Yt - Yt ^
et = residual or forecast error =

15. Forecast Errors
MAD measures forecast accuracy by averaging the absolute value of the forecast errors (n = number of errors and not sample size). Magnitude of errors.
MSE (Mean Squared Error) - each error is squared, then summed and divided by the number of observations (errors). Identifies large forecasting errors because of the squares
MAPE (Mean absolute percentage error) - percentages. Find the MAD for EACH period then divide by actual of that period and dividing the sum by the number of errors. How large the forecast errors are in comparison to the actual values.
MPE (Mean percentage error) - determines bias (close to 0 is unbiased; - is overestimating; + is underestimating)

16. Technique Adequacy
Are the autocorrelation coefficients of the residuals random?
Calculate MAD, MSE, MAPE, & MPE
Are the residuals normally distributed?
Is the technique simple to use?