14 Time series Flashcards

1
Q

examples of time series data

A

Yearly GDP of Norway for a period of 20 years
Daily NOK/Euro exchange rate for past year
Quartertly data on the inflation % unemployment rate in the US from 1957-2005

2
Q

Y_{t-j} is called __

A

jth lag

3
Q

jth lag

A

Y{t-j} is called jth lag

4
Q

Y_{t+j}

A

jth future value

5
Q

the first difference

A

Yt - Y{t-1}

6
Q

Y_t - Y_{t-1}

A

the first difference

7
Q

time series regression models can be used for

A

estimating (dynamic) causal effects

forecasting

8
Q

logarithmic growth

A

logarithmic grow or log-difference:
△ln(Yt) = ln(Yt) − ln(Y{t−1})

(≈ △Yt / Y{t-1})

9
Q

autocorrelation

A

The jth autocorrelation
ρj = Cov(Yt, Y{t − j}) / ￼Var(Yt)

the denominator assumes stationarity of Yt

10
Q

stationarity

A

A time series is stationary if it’s probability distribution does not change over time

When the joint distribution of a time series variable and its lagged values does not change over time

11
Q

forecast error

A

The difference between the value of the variable that actually occurs and its forecasted value:
Y{T+j} − Y{T+j | T}

NOT the same as residual

A forecast Y{T+j | T} and forecast error for j ≥ 1 are “out-of-sample”: They are calculated for some date beyond the data set used to estimate the regression. Y_{T+j} is not observed in the data set used to estimate the regression.

12
Q

RMSFE

A

Root mean squared forecast error

RMSFE = sqrt( E[ (Y{T+1} − Y{T+1 | T})^2 ] )

13
Q

AR(1)

A

First-order autoregressive model:
Yt = β0 + β1Y{t−1} + ut

Forecast in next period based on AR(1) model:
Y{T+1 | T} = β0 + β1Y_T

14
Q

AR(p)

A

The pth order autoregressive model:
Yt = β0 + β1Yt−1 + β2Yt−2 + … + βpYt−p + ut

The number of lags p is called the order or lag length of the autoregression.

15
Q

(AR(p))

We can use ___ to determine the lag order p

A

(AR(p))
We can use t- or F-tests to determine the lag order p
(or using an information criterion: BIC, AIC)

16
Q

A

Autoregressive distributed lag model

A linear regression model in which the time series variable Yt is expressed as a function of lags of Yt and of another variable, Xt.

The model is denoted ADL(p, q), where p denotes the number of lags of Yt and q denotes the number of lags of Xt.

17
Q

Granger causality test

A

A procedure for testing whether current and lagged values of one time series help predict future values of another time series

18
Q

two types of trends

A

Deterministic trend
Yt = β0 + λt + u1
(series is a nonrandom function of time)

Stochastic trend
Yt = β0 + Y{t−1} + u1
(series is a random function of time)

19
Q

random walk

A

A time series process in which the value of the variable equals its value in the previous period plus an unpredictable error term:

Yt = Y{t-1} + ut
where ut is i.i.d.

20
Q

random walk with drift

A

A generalization of the random walk in which the change in the variable has a nonzero mean but is otherwise unpredictable.
Yt = β0 + Y{t-1} + ut

A random walk is nonstationary, as the distribution is not constant over time. The variance of a random walk increases over time:
Var(Yt) = Var(Y{t−1}) + Var(u{t})

21
Q

If Yt follows and AR(p) model, Yt is stationary if ___

A

If Yt follows and AR(p) model, Yt is stationary if its roots z are all greater than 1 in absolute value.

The roots are the values of z that satisfy
1 − β{1}z − β{2}z^2 − … − β{p}z^p = 0

22
Q

method for detecting trends

A

Dickey-Fuller test for AR(1)

Yt = β0 + β1Y{t−1} + ut
H0 : β1 = 1 vs H1 : β1

23
Q

unit root

A

an autoregression with a largest root equal to 1

24
Q

Instead of testing the null hypothesis of a stochastic trend against the alternative hypothesis of no trend….

A

…the alternative hypothesis can be that Yt is stationary around a deterministic trend. The Dickey-Fuller regression then includes a deterministic trend

25
Q

If the series Yt has a stochastic trend, then ___ does not have a stochastic trend.

A

If the series Yt has a stochastic trend, then the first difference of the series △Yt does not have a stochastic trend.