Time Series Analysis Flashcards

1
Q

A time series

A

set of observations for a variable over time

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2
Q

time series model

A

captures the time-series pattern and allows us to make predictions about the variable in the future.

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3
Q

primary limitation of trend models

A

not useful if the residuals exhibit serial correlation.

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4
Q

autoregressive model (AR)

A

dependent variable is regressed against one or more lagged values of itself

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5
Q

dependent variable is regressed against one or more lagged values of itself

A

time series being modeled is covariance stationary

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6
Q

A time series is covariance stationary if it satisfies the following three conditions:

A

 1- Constant and finite expected value.
 2- Constant and finite variance.
 3- Constant and finite covariance

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7
Q

one-period-ahead forecast for an AR(1) model

A

xt+1=b0+b1xt

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8
Q

two-step-ahead forecast for an AR(1) model

A

xt+2=b0+b1xt+1

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9
Q

When an AR model is correctly specified, the residual terms

A

will not exhibit serial correlation

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10
Q

Serial correlation (or autocorrelation) means the error terms

A

positively or negatively correlated.

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11
Q

When the error terms are correlated

A

standard errors are unreliable and t-tests can incorrectly show statistical significance or insignificance.

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12
Q

mean reversion

A

tendency to move toward its mean

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13
Q

mean reversion formula

A

xt=b0(1−b1)

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14
Q

root mean squared error(RMSE)

A

accuracy of autoregressive models in forecasting out-of-sample values

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15
Q

lower RMSE for the out-of-sample data

A

lower forecast error and will be expected to have better predictive power in the future.

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16
Q

The procedure to test whether an AR time-series model is correctly specified involves three steps:

A

1-Estimate the AR model being evaluated using linear regression.
2-Calculate the autocorrelations of the model’s residuals.
3-Test whether the autocorrelations are significant.

17
Q

Random Walk

A

the predicted value equals the value of the series in the previous period plus a random error term.

18
Q

random walk equation

A

xt = xt–1 + εt

19
Q

Random Walk with a Drift Equation

A

xt = b0 + b1xt–1 + εt

20
Q

Random Walk with a Drift

A

the intercept term is not equal to zero.

21
Q

Neither a random walk nor a random walk with a drift exhibits

A

covariance stationarity

22
Q

a random walk, with or without a drift, exhibits

A

unit root (b1 = 1).

23
Q

A time series has a unit root if

A

the coefficient on the lagged dependent variable is equal to one.

24
Q

To determine whether a time series is covariance stationary

A

(1) run an AR model and examine autocorrelations, or
(2) perform the Dickey Fuller test.

25
Q

first differencing

A

If we believe a time series is a random walk (i.e., has a unit root), we can transform the data to a covariance stationary using first differencing

26
Q

Seasonality in a time series is tested by

A

calculating the autocorrelations of error terms.

27
Q

autoregressive conditional heteroskedasticity (ARCH)

A

problem associated with the correlation of variances of the error terms

28
Q

autoregressive conditional heteroskedasticity (ARCH) exists if

A

the variance of the residuals in one period is dependent on the variance of the residuals in a previous period

29
Q

he ARCH(1) regression model is expressed as:

A

ε2t =a0+a1ˆε2t−1+μt

If a1, is statistically different from zero, the time series is ARCH(1).

30
Q

ARCH model can be used to predict the variance of the residuals in future periods

A

σ2t+1=a0+a1ε2t

31
Q

Cointegration

A

means that two time series are economically linked or follow the same trend and that relationship is not expected to change

32
Q

To test whether two time series are cointegrated

A

(1) if neither time series has a unit root, then the regression can be used;
(2) if only one series has a unit root, the regression results will be invalid;
(3) if both time series have a unit root and are cointegrated, then the regression can be used;
(4) if both time series have a unit root but are not cointegrated, the regression results will be invalid.

33
Q

to determine whether two times series are cointegrated.

A

Dickey Fuller test with critical t-values is used

34
Q

RMSE equals

A

the square root of the average squared error.