Introduction to Time Series Forecasting

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Introduction to Time Series Forecasting

• Bernard Menezes
• with inputs from
• Kalam, Pankaj, Somsekhar, Timma

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Time Series

• A sequence of observations of a quantifiable
  phenomenon recorded in increasing order of time

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Time Series - Examples

• Stock price, Sensex
• Exchange rate, interest rate, inflation rate,
  national GDP
• Retail sales
• Electric power consumption
• Number of accident fatalities

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Goals

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

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Forecasting vs. Extrapolation
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Error Measures

• RMSE
• MAE
• MAPE
• Max error

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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)

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Stationarity

• Should we care?
• Strict stationarity, covariance stationarity

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Covariance, ACF, PACF

• What do these tell us?

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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
• Whats the point?

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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

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Cyclical Component?

• Generally trend and the cyclical component are
  analyzed/estimated together for ease of model
  construction

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Experiment 1 MAPEs for different models
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Experiment 2 Does Decomposition help?

• indicates use of decomposition.

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With and without Decomposition
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With and without Decomposition (contd.)
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Experiment 3 Which error measure do we use for
the decomposed series?
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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?

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AR1

• 0.5X(t-1)eps(t)

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AR1

• 0.9X(t-1)eps(t)

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AR1

• 0.2X(t-1)eps(t)

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AR2

• 0.3X(t-1)0.5X(t-2)eps(t)

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MA1

• 0.8eps(t-1)eps(t)

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