Incorporating Seasonality

• Modeling seasonality with trend

• Forecasting

Seasonality

• Data = Trend + Season (Quarter, say) +

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I II III IV IV IV

Defining Dummy Variables

Dummy Variables

Quarter I

Quarter II

Quarter III

Quarter IV

Q1

1

0

0

0

Q2

0

1

0

0

Q3

0

0

1

0

Q4

0

0

0

1

Eviews: @seas

Seasonal Model - 1for Quarterly Data

Note: Q4 is not included

Yt = + 1Q1t + 2Q2t + 3Q3t + t

Interpretation of the Model

Quarter Model

I Yt = 0+1 + t

II Yt = 0+2 + t

III Yt = 0+3 + t

IV Yt = 0 + t

Seasonal Model – 2for Quarterly Data

Yt = 1Q1t + 2Q2t + 3Q3t + 4Q4t+t

Note: 0 is not included

Interpretation of the Model

Quarter Equation ( is omitted)

I Yt = 1 + t

II Yt = 2 + t

III Yt = 3 + t

IV Yt = 4 + t

Model for Trend and Seasonality-1

Yt = +1 t +1Q1t + 2Q2t + 3 Q3t + t

Note: Q4 is not included

Interpretation of the Model

Quarter Equation ( is omitted)

I Yt = 0+ 1t + 1 +t

II Yt = 0+ 1t + 2 + t

III Yt = 0+ 1t + 3 + t

IV Yt = 0 + 1t + t

Model for Trend and Seasonality-2

Yt = 1 t +1Q1t + 2Q2t + 3 Q3t + 4 Q4t + t

Note: 0 is not included

Interpretation of the Model

Quarter Equation

I Yt = 1t + 1 + t

II Yt = 1t + 2 + t

III Yt = 1t + 3 + t

IV Yt = 1t + 4 + t