1. Introduction to Time Series Forecasting
Bernard Menezes
with inputs from
Kalam, Pankaj, Somsekhar, Timma

2. Time Series
A sequence of observations of a quantifiable phenomenon recorded in increasing order of time

3. Time Series - Examples Stock price, Sensex
Exchange rate, interest rate, inflation rate, national GDP
Retail sales
Electric power consumption
Number of accident fatalities

4. Goals To UNDERSTAND the observed series
To look into the future (by deducing from the observed patterns in the past)

5. Forecasting vs. Extrapolation

6. Error Measures
RMSE
MAE
MAPE
Max error

7. Patterns in the data Trend (linear, quadratic, S-shaped, etc.)
Seasonality (by month or quarter of the year, day of the week or time of the day)
Cyclicity (fashions come and go – notice the kinds of spectacle frames “fashionable” over the years)

8. Stationarity Should we care?
Strict stationarity, covariance stationarity

9. Covariance, ACF, PACF
What do these tell us?

10. Series Decomposition
Many time series can be decomposed into following components
Trend (T): Non-periodic component of time series
Cyclical (C): Periodic component with period longer than seasonal period
Seasonal (S): Recurring pattern (periodic component).
Irregular (I): Residual after removing all three components above
What’s the point?

11. Some Models for Decomposition
Trend, seasonality and irregular component can combine in various ways such as
Model 1: T * S * I
Model 2: T * (S + I)
Model 3: T + S + I
The multiplicative model is more appropriate for demand sales

12. Cyclical Component?
Generally trend and the cyclical component are analyzed/estimated together for ease of model construction

13. Experiment 1: MAPEs for different models

15. Experiment 2: Does Decomposition help?
*indicates use of decomposition.

16. With and without Decomposition

17. With and without Decomposition (contd.)

18. Experiment 3: Which error measure do we use for the decomposed series?

23. Factoring expert advice
How many experts do we select?
Which of these is used for a particular point forecast?
How do we weigh the advice of the experts?
Do we dynamically change the above? How? Why?

26. AR1
0.5*X(t-1)+eps(t)

28. AR1
0.9*X(t-1)+eps(t)

30. AR1
0.2*X(t-1)+eps(t)

32. 0.3*X(t-1)+0.5*X(t-2)+eps(t)
AR2
0.3*X(t-1)+0.5*X(t-2)+eps(t)

34. MA1
0.8*eps(t-1)+eps(t)