4.1 Introduction to Time Series

Section 4.1 of Exam MAS-II

Define:

• {Xₜ}

• mₜ

• sₜ

• xₜ

• g

• k

• cₖ

• rₖ

• cₖ(x, y)

• rₖ(x, y)

• Time series

• Trend

• Seasonal variation

• Random patterns

• Seasonal base

• Lag

• Lag k sample autocovariance

• Lag k sample autocorrelation

• Lag k sample cross-covariance

• Lag k sample cross-correlation

The three main decomposition models are:

A multiplicative model can be converted into an ________ model by taking the _______ of both sides.

A multiplicative model can be converted into an additive model by taking the logarithm of both sides.

Stationarity: A stochastic process is second-order stationary if the following two conditions are met:

Decomposition of Series: Using a centered moving average, the monthly trend is:

Additive Seasonality: To estimate average additive seasonality components,

Multiplicative Seasonality: To estimate average multiplicative seasonality components,

Autocorrelation:

c_k =

r_k =

A correlogram plots ___ against and can be used to determine if any statistically significant ___________ exist in a time series.

A correlogram plots r_k against k and can be used to determine if any statistically significant autocorrelations exist in a time series.

Cross-Correlation

c_k(x,y) =

r_k(x,y) =