Question 1

The time series component that reflects a wavelike pattern describing a long-term trend that is generally apparent over a number of years is called cyclical.

Accepted Answer

The cyclical component of a time series refers to the long-term wavelike pattern that occurs over a period of several years, reflecting fluctuations in the economy or other economic factors. This component is distinct from other components, such as trend and seasonal patterns. Therefore, the statement is true.

Question 2

A trend is one of the four different components of a time series.It is a long-term,relatively smooth pattern or direction exhibited by a series,and its duration is more than one year.

Accepted Answer

A trend is indeed a long-term, relatively smooth pattern exhibited by a time series, and its duration typically exceeds one year.

Question 3

The cyclical variation component of a time series measures the over-all general directional movement over a long period of time.

Accepted Answer

The cyclical variation component of a time series represents the repeating pattern of ups and downs that occur over a long period of time. The component that measures the overall general directional movement is the trend component.

Question 4

Random variation is one of the four different components of a time series.It is caused by irregular and unpredictable changes in a time series that are not caused by any other component.It tends to mask the existence of the other more predictable components.

Accepted Answer

Random variation is indeed caused by unpredictable and irregular changes in a time series that are not caused by any other component, and it can make it difficult to identify the other more predictable components of the series.

Question 5

In forecasting,we use data from the past in predicting the future value of the variable of interest.

Accepted Answer

Yes, in forecasting we use historical data points to make projections or predictions about future values of the variable of interest. This involves analyzing patterns and trends in the past data to estimate what is likely to happen in the future.

Question 6

The time series component that reflects a long-term,relatively smooth pattern or direction exhibited by a time series over a long time period is called seasonal.

Accepted Answer

The time series component that reflects a long-term, relatively smooth pattern or direction exhibited by a time series over a long time period is called trend. Seasonal refers to patterns that repeat over a shorter time period, such as days, weeks, or months.

Question 7

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 8

Any variable that is measured over time in sequential order is called a time series.

Accepted Answer

A time series is defined as a collection of observations collected over time, usually at evenly spaced intervals. These observations can represent any variable that changes over time, such as stock prices, economic indicators, or weather patterns. Therefore, any variable that is measured over time in sequential order is considered a time series.

Question 9

In exponentially smoothed time series,the smoothing constant w is chosen on the basis of how much smoothing is required.In general,a small value of w such as 0.1 results in very little smoothing,while a large value of w such as 0.8 results in too much smoothing.

Accepted Answer

In exponentially smoothed time series, a small value of w (e.g., 0.1) results in more smoothing because it gives more weight to past observations, while a large value of w (e.g., 0.8) results in less smoothing because it gives more weight to the most recent observation.

Question 10

The equation: S_t = w⋅y_t + (1 −w)⋅St−₁ (for t≥ 2)refers to exponentially smoothed time series.

Accepted Answer

The equation is indeed the formula for exponentially smoothed time series, where S_t is the smoothed value at time t, w is the smoothing constant, y_t is the actual value at time t, and St−₁ is the smoothed value at time t-1.

Question 11

Seasonal variation is one of the four different components of a time series.These are cycles that occur over short repetitive calendar periods and,by definition,have duration of less than one year.

Accepted Answer

Seasonal variation refers to cycles that occur over short repetitive calendar periods and have a duration of less than one year. Therefore, the statement is true.

Question 12

The purpose of using the moving average is to take away the short-term seasonal and random variation,leaving behind a combined trend and cyclical movement.

Accepted Answer

The statement is true. The moving average is a commonly used technique in time series analysis to smooth out the fluctuations in data and highlight the underlying trend and cyclical component, which can be useful for forecasting and decision-making. By calculating the average of a certain number of past observations, the moving average reduces the impact of short-term noise and variation, revealing the longer-term pattern in the data.

Question 13

One of the simplest ways to reduce random variation is to smooth the time series using moving averages and exponential smoothing.

Accepted Answer

Smoothing techniques such as moving averages and exponential smoothing can reduce random variation by averaging out fluctuations over time.

Question 14

Given a data set with 15 yearly observations,there are only thirteen 3-year moving averages.

Accepted Answer

A 3-year moving average requires at least 2 years before and after a given year to calculate, so for the first and last years in the dataset, it's not possible to calculate a 3-year moving average, resulting in only thirteen 3-year moving averages for a dataset with 15 yearly observations.

Question 15

The effect that business recessions and prosperity have on time series values is an example of the disaster component of a time series.

Accepted Answer

The effect of business recessions and prosperity on time series values is an example of the cyclical component of a time series, not the disaster component. The disaster component refers to unexpected and rare events such as natural disasters, terrorist attacks, or other catastrophes that can have a sudden and extreme impact on the time series.

Question 16

Smoothing time series data by the moving average method or exponential method is an attempt to dampen the effects of seasonal variation.

Accepted Answer

Smoothing time series data by the moving average method or exponential method is primarily aimed at reducing noise and short-term fluctuations, not specifically at dampening seasonal variations.

Question 17

Given a data set with 15 yearly observations,there are only seven 9-year moving averages.

Accepted Answer

The answer of Given a data set with 15 yearly...

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. "Seasonal variation" can refer to traditional seasons as well as other patterns that occur within shorter timeframes.

Question 19

The time series component that reflects the irregular changes in a time series that are not caused by any other component,and tends to hide the existence of the other more predictable components,is called random variation.

Accepted Answer

Random variation, also known as noise or residual, is the component of a time series that cannot be explained or predicted by the other components such as trend, seasonality or cyclical variation. It represents the random fluctuations that are inherent in any data and can obscure the signal or pattern in the other components. Therefore, the statement is true.

Question 20

To calculate the five-period moving average for a time series,we average the value in that time period,the values in the two preceding time periods,and the values in the two following time periods.

Accepted Answer

The statement accurately describes the calculation of a five-period moving average for a time series.

Quiz 20: Time-Series Analytics and Forecasting