# 14 Time series Flashcards

examples of time series data

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

Y_{t-j} is called __

jth lag

jth lag

Y{t-j} is called jth lag

Y_{t+j}

jth future value

the first difference

Yt - Y{t-1}

Y_t - Y_{t-1}

the first difference

time series regression models can be used for

estimating (dynamic) causal effects

forecasting

logarithmic growth

logarithmic grow or log-difference:

△ln(Yt) = ln(Yt) − ln(Y{t−1})

(≈ △Yt / Y{t-1})

autocorrelation

The jth autocorrelation

ρj = Cov(Yt, Y{t − j}) / ￼Var(Yt)

the denominator assumes stationarity of Yt

stationarity

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

forecast error

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.

RMSFE

Root mean squared forecast error

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

AR(1)

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

AR(p)

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.

(AR(p))

We can use ___ to determine the lag order p

(AR(p))

We can use t- or F-tests to determine the lag order p

(or using an information criterion: BIC, AIC)