Question 1

Seasonality is a time-series component.

Accepted Answer

Seasonality is a time-series component that refers to regular and predictable patterns that repeat at fixed intervals within a time series. These patterns can be on a yearly, monthly, weekly, or daily basis and can impact sales, demand, or other variables over time.

Question 2

The location in time of the members of the series of moving averages corresponds precisely with that of the members of the original series.

Accepted Answer

Moving averages are calculated by averaging data points over a specific period, and this process inherently leads to a lag because the average at any point is based on past data, not aligning precisely with the original series' time location.

Question 3

Exponential smoothing is appropriate when the series is nonseasonal and has no consistent upward or downward trend.

Accepted Answer

Exponential smoothing is most effective for time series data that does not exhibit strong trend or seasonal patterns, making it suitable for nonseasonal series without consistent trends.

Question 4

Simple exponential smoothing provides a forecast based on a weighted average of current and past values.

Accepted Answer

Simple exponential smoothing uses a weighted average of current and past values to provide a forecast. The weights decrease exponentially as the values get farther from the present, giving more weight to recent data.

Question 5

Given a data set with 20 yearly observations,there are only twelve 9-year moving averages.

Accepted Answer

A 9-year moving average requires 9 consecutive data points to calculate each average. With 20 observations, the first moving average is calculated from observations 1 to 9, the second from 2 to 10, and so on, until the last one from 12 to 20, resulting in 12 moving averages.

Question 6

The irregular component of a time series exhibits a tendency to grow or decrease rather steadily over long periods of time.

Accepted Answer

The irregular component of a time series, also known as the random or residual component, represents unpredictable, random fluctuations that do not follow a pattern and do not exhibit a steady growth or decrease over time.

Question 7

The more modern approach to time-series analysis concentrates on the isolation of the individual components (trend,seasonality,cyclical,and irregular)from a series.

Accepted Answer

The answer of The more modern approach to time-series analysis...

Question 8

If we could characterize time series primarily in terms of trend,seasonal,and cyclical components,then the series would vary smoothly over time,and forecasts could be made using these components.

Accepted Answer

Trend, seasonal, and cyclical components can help to decompose a time series into predictable patterns and enable the construction of a model that can forecast future values based on these components. These components can help to explain the underlying behavior of the series over time and aid in identifying patterns that may be useful in making predictions.

Question 9

Seasonal patterns in a time series constitute one form of regular,oscillatory behavior.

Accepted Answer

Seasonal patterns in time series refer to repeating patterns that occur at regular intervals, such as daily, weekly, monthly, or seasonal. This regular, oscillatory behavior is a form of seasonality that can be observed in many types of data, including economic indicators, weather patterns, and consumer behavior.

Question 10

The choice of a larger smoothing constant α in simple exponential smoothing would place more weight on the most recent value.

Accepted Answer

Simple exponential smoothing assigns weights to past observations, and the larger the smoothing constant α, the more weight is given to the most recent observation. Therefore, choosing a higher value of α would place more weight on the most recent value.

Question 11

The formula that explains simple exponential smoothing is _t = (1 - α) _t_-1 + αx_t for 0 < α < 1.

Accepted Answer

The formula for simple exponential smoothing is correctly written in the given format, and the equation is stating that the forecast for time period t is a weighted average of the actual observation for time period t and the forecast for the previous time period, with the weights determined by the smoothing parameter (alpha).

Question 12

Much of the early work in time-series analysis involves the construction of a formal model,in which various components either are explicitly or implicitly present,to describe the behavior of a data series.

Accepted Answer

The answer of Much of the early work in time-series...

Question 13

We can smooth a time series using the method of moving averages,based on the idea that any large irregular component at any point in time will exert a smaller effect if we average the point with its immediate neighbors.

Accepted Answer

This is a correct statement and describes the basic concept behind using moving averages to smooth a time series.

Question 14

We calculate the three-period moving average for a time series for all time periods except the first period.

Accepted Answer

The three-period moving average cannot be calculated for the first two periods because there are not enough previous data points (you need at least three data points to calculate a three-period moving average).

Question 15

The seasonal component in a time series reflects a long-term,relatively smooth pattern or direction.

Accepted Answer

The seasonal component in a time series reflects a short-term, repetitive pattern that occurs at regular intervals, such as daily, weekly, or monthly. It is not a long-term, relatively smooth pattern or direction.

Question 16

If x₁,x₂,x₃,... ,x_n are n observations of a time series of interest,a smoothed series can be obtained by using a simple centered 2(m + 1)-point moving average formula: = 2m + 1 (t = m + 1,m + 2,... ,n - m).

Accepted Answer

The answer of If x₁,x₂,x₃,... ,x_n are n observations of...

Question 17

The Holt-Winters Exponential Smoothing procedure allows only the trend component in a time series.

Accepted Answer

The Holt-Winters Exponential Smoothing procedure allows for the estimation of both trend and seasonal components in a time series. It is a widely used method for forecasting time series data in business and economics.

Question 18

The term seasonal variation may refer to the four traditional seasons,or to systematic patterns that occur during a month,a week,or even one day.

Accepted Answer

The statement is true. The term seasonal variation can refer to different types of patterns, including those occurring during traditional seasons or on different time scales.

Question 19

Increasing the value of α from 0.025 to 0.10 in exponential smoothing will increase the weight to the most recent observation by 0.075.

Accepted Answer

The answer of Increasing the value of α from 0.025...

Question 20

Autoregressive forecasting models assume that values in a time series are independent of one another.

Accepted Answer

Autoregressive forecasting models assume that values in a time series are dependent on past values in the series. This dependence is captured through the use of lagged variables in the model.

Quiz 16: Time-Series Analysis and Forecasting