Time Value & ARIMA in R

Question 1

The process of differencing a time series is most effective in dealing with:

a.
Non-constant variance

b.
Constant mean

c.
Linear trends

d.
High autocorrelation

Answer 1

C

Question 2

For a time series to be stationary, which of the following conditions must be met?

a.
The series must have a trend component.

b.
The series must show a seasonal pattern.

c.
The variance of the series must be constant over time.

d.
The mean of the series must be increasing over time.

Answer 2

C

Question 3

In moving average models, ______________________________________ .

a.
current value of dependent variable depends linearly on the current noise terms of independent variables.

b.
current value of dependent variable depends linearly on the current and past values of independent variables.

c.
current value of dependent variable depends linearly on the past values of dependent variables and error term.

d.
current value of dependent variable depends linearly on the current and past values of error terms.

Answer 3

D

Question 4

A white noise process will have

(i) A zero mean

(ii) A constant variance

(iii) Autocovariances that are constant

(iv) Autocovariances that are zero except at lag zero.

A.
(i), (ii), (iii), and (iv)

B.
(i), (ii) and (iv) only

C.
(i) and (iii) only

D.
(i), (ii), and (iii) only

Answer 4

B

Question 5

Which function in R is used to check the frequency of a time series dataset?

a.
acf()

b.
ts.plot()

c.
diff()

d.
frequency()

Answer 5

D

Question 6

In time series analysis, what is the primary purpose of the ‘Partial Autocorrelation Function (PACF)’?

a.
To measure the overall variance in the series

b.
To assess the direct relationship between an observation and its lag

c.
To identify seasonal patterns

d.
To predict future values in the series

Answer 6

B

Question 7

Which of the following best describes a stationary time series?

a.
A series that exhibits clear seasonality and trends

b.
A series with a constant mean, variance, and autocovariance over time

c.
A series with increasing mean and variance over time

d.
A series with mean and variance dependent on time

Answer 7

B

Question 8

Which of the following is not an example of a time series model?

a.
Moving Average

b.
Autoregressive Integrated Moving Average

c.
Autoregressive

d.
No Answer

Answer 8

D

Question 9

The autocorrelation function (ACF) in time series analysis is used to:

a.
Identify the correlation structure of the data

b.
Predict future values

c.
Estimate mean and variance

d.
Transform non-stationary to stationary data

Answer 9

A

Question 10

What is the primary purpose of differencing in time series analysis?

a.
To make the series stationary

b.
To remove the error terms from the model

c.
To introduce seasonality into the series

d.
To increase the mean of the series

Answer 10

A

Question 11

Which of the following best describes an ARIMA model’s approach to non-stationarity?

a.
Applying autocorrelation to enhance non-stationarity.

b.
Ignoring non-stationarity as irrelevant.

c.
Using differencing to transform the series into a stationary one.

d.
Increasing the variance until stationarity is achieved.

Answer 11

C

Question 12

What is a key characteristic of a time series that exhibits a trend?

a.
Periodic fluctuations

b.
Long-run evolution in variables

c.
Constant mean

d.
Constant variance

Answer 12

B

Question 13

Which of the following is true for white noise?

a.
Mean is constant

b.
Variance = 0

c.
Zero autocovariance

d.
Zero autocorrelations except at lag zero

Answer 13

D

Question 14

A stationary time series with a constant autocorrelation structure over time is described as:

a.
Strongly stationary

b.
Random walk

c.
Non-stationary

d.
Weakly stationary

Answer 14

D

Question 15

What is indicated by a gradual decay in the ACF and a sharp cutoff in the PACF?

a.
An MA process is present.

b.
An AR process is present.

c.
The series is over-differenced.

d.
The series is non-stationary.

Answer 15

B

Question 16

What does a lag 2 autocorrelation represent in time series analysis?

a.
Non-stationarity of the series

b.
Correlation between values one time period apart

c.
Independence of the series

d.
Correlation between values two time periods apart

Answer 16

D

Question 17

What does a sharp cutoff in the PACF after lag ‘p’ indicate in an AR(p) process?

a.
The presence of a moving average component.

b.
The need for differencing.

c.
That the series is non-stationary.

d.
The order of the AR process.

Answer 17

D

Question 18

In time series analysis, what is the primary purpose of applying a logarithmic transformation?

a.
To stabilize variance in a series with non-constant variance

b.
To reduce the impact of outliers

c.
To highlight the cyclical components

d.
To detect seasonality more effectively

Answer 18

A

Question 19

If a time series exhibits a regularly repeating pattern of highs and lows, what is this called?

a.
Trend.

b.
Seasonality.

c.
Stationarity.

d.
White noise.

Answer 19

B

Question 20

In time series analysis, what is indicated by a lag 1 autocorrelation?
Question 2Answer

a.
Correlation between values one time period apart

b.
Correlation between values two time periods apart

c.
Non-stationarity of the series

d.
Independence of the series

Answer 20

A

Question 21

You have a process Yt. The first difference process follows a MA(2) model. What is the appropriate model for Yt ?
Question 3Answer

a.
ARIMA(0, 1, 2)

b.
AR(2)

c.
ARIMA(0, 2, 2)

d.
MA(3)

Answer 21

A

MA(2) = ARIMA (0,0,2)
Next Model Would be
ARIMA (0,1,2) b/c of the added differencing

Question 22

What is the purpose of the ACF and PACF plots when fitting a time series model?
Question 4Answer

a.
To identify the order of AR or MA processes.

b.
To visualize the trend in the series.

c.
To check the normality of the residuals.

d.
To confirm the stationarity of the series.

Answer 22

A

Question 23

Which of the following situations can be analyzed using time series methods?

1. Predicting daily rainfall amounts for the upcoming season.
2. Estimating the value of a car based on its mileage and age.
3. Tracking the monthly change in consumer price index over several years.
   Question 5Answer

A.
2 and 3

B.
1, 2, and 3

C.
Only 3

D.
1 and 3

Answer 23

D

Cannot be 2 b/c you are not tracking the cars value day by day. Time series is data linked to causes on a frequent, time series, basis.

Question 24

What role does the logarithm transformation play in time series analysis?
Question 6Answer

a.
To stabilize non-constant variance

b.
To calculate autocorrelation

c.
To enhance seasonal patterns

d.
To increase the trend

Answer 24

A

Question 25

In time series analysis, what does first differencing help to remove? Question 7Answer a. Trend b. Variance c. Correlation d. Mean

Answer 25

A

Question 26

What does the autocorrelation function (ACF) help to identify in a time series? Question 8Answer a. The presence of a trend. b. The need for differencing. c. The seasonality of the series. d. The order of the moving average part.

Answer 26

D

Question 27

What does the PACF plot reveal about an AR(p) model? Question 9Answer a. It will have a sharp cutoff at lag p. b. It identifies the moving average component. c. It indicates the need for differencing. d. It shows that the series is non-stationary.

Answer 27

A

Question 28

Characteristics of a white noise process include (i) Zero mean (ii) Constant variance (iii) Zero autocorrelations for all non-zero lags (iv) Autocovariances that change over time. Question 10Answer A. (i), (ii), (iii), and (iv) B. (i), (ii), and (iii) only C. (ii) and (iv) only D. (i), (iii), and (iv) only

Answer 28

B

Question 29

What does it mean if the residuals of a fitted time series model are white noise? Question 11Answer a. The model has captured the systematic structure in the data. b. The model has not captured any systematic information in the data. c. The model has overfitted the data. d. The model has perfectly predicted all future values.

Answer 29

A

Question 30

Which component in time series analysis is responsible for capturing long-term progression or decline in the data? Question 12Answer a. Seasonal component b. Cyclical component c. Residual component d. Trend component

Answer 30

D

Question 31

Identify the model for the following process: Yt = c + Ø1 Yt-1 + θ1 εt-1 + εt Question 13Answer A. AR(1) B. ARIMA(1, 0, 1) C. ARMA(1, 0) D. ARIMA(0, 1, 1)

Answer 31

B

Question 32

What does the autocorrelation function (ACF) primarily reveal in a time series? Question 14Answer a. The correlation between lagged values of the series b. The mean and variance c. The overall direction of the data d. The presence of a linear trend

Answer 32

A

Question 33

In an ARIMA model, what does the 'I' stand for? Question 15Answer a. Independent. b. Integrated. c. Interval. d. Instantaneous.

Answer 33

B

Question 34

In autoregressive models, ______________________________ . Question 16Answer a. current value of dependent variable is influenced by current values of independent variables. b. current value of dependent variable is influenced by both past values of dependent variables and error term. c. current value of dependent variable is influenced by current and past values of independent variables. d. current value of dependent variable is influenced by current and past values of error terms.

Answer 34

B

Question 35

The first differencing of a time series is primarily used to: Question 17Answer a. Decrease the mean b. Remove the trend c. Increase the variance d. Enhance the trend

Answer 35

B

Question 36

What does the MA(q) process typically capture in time series data? Question 18Answer a. The deterministic components of the series. b. Seasonal fluctuations. c. Long-term trends. d. Richer dynamic patterns through lags of the shock.

Answer 36

D

Question 37

The autocorrelation function in time series analysis is used to assess: Question 19Answer a. The trend of the series b. The seasonality of the series c. The independence of the series d. Whether a series depends on its past

Answer 37

D

Question 38

In a time series, what does stationarity imply about the mean and variance? Question 20Answer a. The mean is constant, but the variance varies. b. The mean and variance increase over time. c. The mean and variance are constant over time. d. The mean varies, but the variance is constant.

Answer 38

C

Question 39

What are the correct statements about ARIMA(p, d, q) models? Question 1Answer a. An ARIMA model is used for non-stationary data. b. The “I” in ARIMA stands for “indifferent.” c. ARIMA includes differencing to remove trends. d. ARIMA models can't handle seasonal components.

Answer 39

C

Question 40

An ARMA(p, q) (p, q are integers bigger than zero) model will have Question 2Answer a. an acf that is zero after p lags and a pacf that is zero after q lags b. an acf that tails off and a pacf that is zero after p lags c. an acf that tails off and a pacf that is zero after q lags d. an acf and pacf that both tail off

Answer 40

D

Question 41

Which of the following is not true for a white noise process? Question 3Answer a. It has a zero mean b. It exhibits autocorrelation c. It has a constant variance d. It is uncorrelated

Answer 41

B

Question 42

What does the presence of significant spikes at lags 1, 2, and 3 in the ACF suggest about a time series model? Question 4Answer a. That an AR(3) model is appropriate. b. That there is a seasonal component with a period of 3. c. That an MA(3) model is appropriate. d. That differencing should be applied three times.

Answer 42

C

Question 43

Which of the following is a key characteristic of stationary time series data? Question 5Answer a. Increasing trend b. Constant variance over time c. Linear growth d. Periodic fluctuations

Answer 43

B

Question 44

An overall upward or downward pattern in a time series is known as: Question 6Answer a. Trend component b. Irregular component c. Cyclical component d. Seasonal component

Answer 44

A

Question 45

What is the primary purpose of using seasonal differencing in time series analysis? Question 7Answer a. To calculate the mean b. To enhance the trend c. To address seasonality in the data d. To identify irregular components

Answer 45

C

Question 46

What is the distinguishing feature of the ACF in an AR(1) process with a positive coefficient of AR component? Question 8Answer a. It alternates between positive and negative. b. It decreases exponentially as lag increases. c. It remains constant at all lags. d. It increases exponentially over time.

Answer 46

B

Question 47

In time series analysis, what does the end() function in R determine? Question 9Answer a. The last autocorrelation coefficient b. The end time of the series c. The ultimate trend in the data d. The final value of the series

Answer 47

B

Question 48

In the context of ARIMA models, the term 'integrated' refers to which of the following? Question 10Answer a. The use of differencing to stabilize the series b. The inclusion of seasonal components c. The integration of independent variables d. The combination of AR and MA parts

Answer 48

A

Question 49

What does the ARIMA model imply if a series becomes stationary after first differencing? Question 11Answer a. The series is inherently non-stationary and cannot be modeled. b. The differenced series is modeled as an ARMA process. c. The series requires at least two differencing operations. d. The series is best modeled as an ARIMA(0, 0, 0).

Answer 49

B

Question 50

What is the primary purpose of time series analysis? Question 12Answer a. To apply differencing until the series becomes non-stationary. b. To eliminate all autocorrelations in the data. c. To predict future values of the series based on past values and errors. d. To ensure data is not stationary.

Answer 50

C

Question 51

What is the typical purpose of the ts.plot() function in time series analysis using R? Question 13Answer a. To calculate autocorrelations b. To plot multiple time series together c. To identify stationary processes d. To perform linear regression

Answer 51

B

Question 52

A random walk process is characterized by: Question 14Answer a. Dependence on past values and white noise error b. Predictable changes c. Constant variance d. Seasonal patterns

Answer 52

A

Question 53

What is indicated by a flat-looking time series with no periodic fluctuations? Question 15Answer a. Seasonality b. Non-stationarity c. Weak stationarity d. Trend component

Answer 53

C

Question 54

What indicates a good fit of an ARMA model when checking the ACF of the residuals? Question 16Answer a. Residuals are close to 0, indicating white noise. b. Large residuals that highlight model accuracy. c. Increasing trend in the residuals. d. Seasonal patterns in the residuals.

Answer 54

A

Question 55

What pattern does the ACF of an AR(1) process with a positive coefficient of the AR component display? Question 17Answer a. A sinusoidal pattern. b. Constant autocorrelation at all lags. c. An exponential decay as lag increases. d. A sharp cutoff after lag 1.

Answer 55

C

Question 56

What does the Autocorrelation Function (ACF) help identify in time series data? Question 18Answer a. Correlation structure b. Mean c. Randomness d. Variance

Answer 56

A

Question 57

Which term best describes a time series that does not exhibit significant trends, seasonality, or cyclical patterns? Question 19Answer a. White noise b. Exponential c. Non-stationary d. ARIMA

Answer 57

A

Question 58

What is the primary purpose of the frequency() function in time series analysis using R? Question 20Answer a. To identify the number of observations per unit time b. To determine the trend component c. To calculate the average value of the series d. To estimate the variance

Answer 58

A

Question 59

The partial autocorrelation function in time series analysis is useful for: Question 1Answer a. Determining the dependence on past values b. Identifying the seasonal component c. Estimating the trend component d. Assessing the overall variability

Answer 59

A

Question 60

Which of the following statements are true concerning the class of ARIMA(p, d, q) models? (i) An ARIMA(p, 1, q) model is equivalent to an ARMA(p, q) model estimated on a series that has been differenced once. (ii) The “I” stands for integrated. (iii) Optimal value of d in an ARIMA(p, d, q) model for financial time series could be 2 or 3. Question 2Answer A. (ii) and (iii) only B. (i) and (ii) only C. (i), (ii), and (iii) D. (i) and (iii) only

Answer 60

B

Question 61

What does autocorrelation measure? Question 3Answer a. Degree of correlation between multiple points on the different series observed at different times. b. Linear dependence between two points on different series observed at same time. c. Degree of correlation between two points on the same series observed at different times. d. Quadratic dependence between two points on the same series observed at different times.

Answer 61

C

Question 62

What is the main purpose of differencing a time series data? Question 5Answer a. To remove trend and seasonality b. To increase the mean c. To stabilize the variance d. To forecast future values

Answer 62

A

Question 63

What would a time series with no autocorrelation at any lag suggest? Question 6Answer a. The series is a random walk. b. The series has a strong seasonal pattern. c. The series is perfectly predicted by an AR model. d. The series may be white noise.

Answer 63

D

Question 64

In a time series, what does the presence of a linear increasing trend usually suggest? Question 7Answer a. There is high seasonality b. The need for differencing to achieve stationarity c. The series is weakly stationary d. The series is stationary

Answer 64

B

Question 65

An overall upward or downward pattern in an annual time series would be contained in which component of the time series? Question 8Answer a. Irregular b. Cyclical c. Seasonal d. Trend

Answer 65

D

Question 66

What does an AR(1) process illustrate about the series Xt? Question 9Answer A. Xt is a non-linear function of the errors. B. Xt is a linear function of its value at time t-2. C. Xt is a linear function of its value at time t-1. D. Xt is independent of its past values.

Answer 66

C

Question 67

How can you tell if an ARMA model's residuals look like white noise? Question 10Answer a. The residuals display a clear increasing or decreasing trend. b. No autocorrelations exist at any lag. c. The residuals vary widely from 0. d. There are significant autocorrelations at all lags.

Answer 67

B

Question 68

What type of process is a white noise process in time series analysis? Question 11Answer a. Seasonal b. Non-stationary c. Stationary d. Trending

Answer 68

C

Question 69

Which of the following is a characteristic of a white noise process? Question 12Answer a. Uncorrelated random variables b. Constant autocorrelation c. Increasing variance over time d. Non-zero mean

Answer 69

A

Question 70

Which of the following transformations can stabilize a time series with non-constant variance? Question 13Answer a. Logarithm b. Linear regression c. Differentiation d. Exponential smoothing

Answer 70

A

Question 71

In time series analysis, a cyclical trend is most likely observed in: Question 14Answer a. Seasonal variations b. Random fluctuations c. Business cycles d. Regular repeating patterns

Answer 71

C

Question 72

In a weakly stationary process, the autocorrelation structure is: Question 15Answer a. Constant over time b. Zero at all lags c. Non-constant over time d. Increasing over time

Answer 72

A

Question 73

What is the main feature of a white noise process in time series analysis? Question 16Answer a. Predictable pattern b. Constant and high autocorrelation c. Zero mean and constant variance d. Mean reversion

Answer 73

C

Question 74

What is the effect of first differencing on a time series with a linear trend? Question 17Answer a. Converts the trend to a nonlinear form b. No effect on the trend c. Increases the trend d. Removes the trend

Answer 74

D

Question 75

What is the following model about? Xt = 0.1 + 0.2Xt-1 + 0.1Xt-2 + εt-1 + εt-2 + εt εt ~ wn(0, σ2) Question 18Answer A. ARIMA(2, 1, 3) B. ARMA(2, 3) C. ARMA(2, 1) D. ARIMA(2, 0, 2)

Answer 75

D

Question 76

How does the variance of a random walk process behave over time? Question 19Answer a. It increases b. It decreases c. It remains constant d. It oscillates

Answer 76

A

Question 77

In the context of time series data, which term best describes a pattern that repeats over a known, fixed period? Question 20Answer a. Cyclical b. Irregular c. Trend d. Seasonality

Answer 77

D