Seasonal Index and Housing Sales Data Analysis

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Questions and Answers

What is the primary difference between the additive and multiplicative decomposition procedures in time series analysis?

The method of calculation for the trend component

The use of differences versus ratios (correct)

The type of data used

The order in which the components are estimated

Which time series component is calculated by subtracting the estimated trend, cycle, and seasonality from the original data series?

Trend component

Irregular component (correct)

Cyclical component

Seasonal component

What is the purpose of using a centered moving average in time series analysis?

To estimate the seasonal component

To remove non-stationarity in the data

To smooth out the irregular component

To estimate the trend component (correct)

What is the primary advantage of using a time series decomposition plot?

It provides a visual representation of the time series components Signup and view all the answers

What is the definition of stationarity in the context of time series analysis?

A time series with constant mean and variance over time Signup and view all the answers

Which of the following is NOT a component of a time series in the classical decomposition method?

Residual component Signup and view all the answers

What is the primary purpose of pseudo-additive decomposition in time series analysis?

To handle series with one exceptional month or quarter Signup and view all the answers

Which of the following components is related to the economic health and confidence of the nation?

Trend-cycle component Signup and view all the answers

What is the purpose of a decomposition plot in time series analysis?

To visualize the decomposition procedure Signup and view all the answers

What is the name of the method used to obtain the estimates of the cyclical, seasonal, and irregular components in Figure 1?

STL method Signup and view all the answers

Which of the following is a characteristic of a time series that exhibits stationarity?

Constant mean and variance over time Signup and view all the answers

What is the term for the remaining component after the trend and seasonal components have been removed from a time series?

Irregular component Signup and view all the answers

What is the primary reason for using a multiplicative decomposition in this time series analysis?

To account for the increasing seasonal variation as the level of the series increases Signup and view all the answers

What is the purpose of calculating the ratio of the data to the centered 12-month MA values?

To decompose the time series into its trend-cycle, seasonal, and irregular components Signup and view all the answers

Why are six values missing at the beginning and six values missing at the end of the centered 12-month MA calculation?

Due to the averaging procedure used in the calculation Signup and view all the answers

What is the advantage of using a centered 12-month MA over a simple MA?

It provides a more robust estimate of the trend-cycle component Signup and view all the answers

What is the mathematical representation of the ratio of the actual data to the moving average values?

Rt = St / Tt Signup and view all the answers

What is the primary component of the time series that is isolated through the calculation of the ratio of the data to the centered 12-month MA values?

Seasonal component Signup and view all the answers

Study Notes

Time Series Decomposition

Time series decomposition is a method to break down a time series into its component parts
The goal is to separate a time series into trend, seasonal, and irregular components

Additive Decomposition

In additive decomposition, the components are added together to obtain the original time series
The formula is: Yt = Tt + St + Et
The steps to perform additive decomposition are:
- Step 1: Compute the trend-cycle component (Tt) using a centered moving average
- Step 2: Compute the seasonal component (St) by taking the average of the de-trended values for each month
- Step 3: Construct the seasonal component by stringing together the seasonal indices for each year
- Step 4: Compute the irregular component (Et) by subtracting the estimated seasonality, trend, and cycle from the original data series

Multiplicative Decomposition

In multiplicative decomposition, the components are multiplied together to obtain the original time series
The formula is: Yt = Tt * St * Et
The method is often called the “ratio-to-moving averages” method
The steps to perform multiplicative decomposition are similar to additive decomposition, but ratios are taken instead of differences

Pseudo-Additive Decomposition

Pseudo-additive decomposition is useful for series with one month or quarter that is much higher or lower than the others
The formula is: Yt = Tt * (St + Et - 1)
This type of decomposition is not discussed in detail in the provided text

Decomposition Plots

A decomposition plot is a graph that shows the original time series and its component parts
Decomposition plots are helpful in visualizing the decomposition procedure
The plot is obtained by adding the three components (trend-cycle, seasonal, and irregular) together

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Description

Explore the process of determining seasonal indices for housing sales data and constructing the seasonal component. Learn how to compute the irregular series by subtracting estimated seasonality, trend, and cycle from the original data series. Dive into de-trended housing sales data analysis with detailed steps and figures.