Time Series Analysis: Seasonal and Trending Behavior

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What is the primary characteristic of seasonal variations in time series data?

Random fluctuations

Increasing trend over time

Periodic patterns (correct)

Irregular downward trend

Which component of a time series represents irregular fluctuations that cannot be attributed to trend and seasonal patterns?

Seasonal component

Residual component (correct)

Trend component

Linear trend

What is the purpose of classical decomposition models in time series analysis?

To separate a time series into its trend, seasonal, and residual components (correct)

To forecast future values in a time series

To identify patterns in scattered data

To visualize data in a scatterplot

What is the apparent trend observed in the scatterplot of Figure 3.7?

An increase in passenger numbers over the years (D) Signup and view all the answers

What type of time series plot is typically used to visualize data with seasonal patterns?

Time plot (A) Signup and view all the answers

What can be inferred from the presence of residual fluctuations in a time series?

There are unexpected variations or external influences not captured by the trend and seasonal components (D) Signup and view all the answers

What is the main purpose of classical decomposition models in time series analysis?

To separate the different components of a time series (B) Signup and view all the answers

What type of pattern can be observed in the scatterplot of Figure 3.7?

Seasonal pattern (A) Signup and view all the answers

What is the main difference between a seasonal component and a trend component in a time series?

The seasonal component is periodic, while the trend component is not (A) Signup and view all the answers

What is the equation for an additive model in classical decomposition?

Xt = mt + st + et (C) Signup and view all the answers

What can be observed in the seasonal plot of Figure 3.8?

A seasonal pattern over the months (D) Signup and view all the answers

What is the purpose of separating the components of a time series using classical decomposition models?

To analyze each component separately (A) Signup and view all the answers

What is the purpose of seasonally adjusting an economic indicator such as unemployment percentages?

To reveal the trend that might otherwise be hidden by seasonal variation (C) Signup and view all the answers

How can we ensure that the estimated seasonal factors add up to zero in an additive decomposition model?

By dividing the sum of the seasonal estimates by the seasonality period (D) Signup and view all the answers

What type of decomposition model is assumed when the seasonal factors are adjusted to add up to zero?

Additive decomposition model (D) Signup and view all the answers

How can we calculate the seasonally adjusted series in an additive decomposition model?

Xt - ŝt (D) Signup and view all the answers

What is the benefit of using the moving-average procedure to analyze time series data?

It successfully describes the time series but does not allow for forecasting (D) Signup and view all the answers

What is the purpose of calculating the value w in the process of adjusting seasonal factors?

To adjust each seasonal factor (B) Signup and view all the answers