Time Series

Question 1

time series

Answer 1

gives us value of the same variable Y at different time periods

Question 2

lags

Answer 2

Yt-1, Yt-2 etc

Question 3

first difference

Answer 3

change in value of Y between time t-1 and t

Question 4

autocorrelated

Answer 4

when a series is correlated with its lags

Question 5

volatility clustering

Answer 5

when there are periods of high volatility followed by periods of low volatility

Question 6

breaks

Answer 6

abrupt or occur slowly due to econ policy or changes in structure of economy

Question 7

serial correlation (autocorrelation)

Answer 7

correlation between error terms (at time t, t-1, t-2 etc) in regression model

Question 8

exogeneity assumption

Answer 8

ut must be uncorrelated with all xts i.e. all explanatory variables (X) cannot respond to change in/past values of dependent variable (Y)

Question 9

no autocorrelation assumption

Answer 9

e.g if interest rate is unexpectedly high in one period it shouldn’t be high in the next period too

Question 10

consequences of autocorrelation

Answer 10

OLS no longer BLUE

OLS se underestimated - CI too narrow - t ratio too large - p values too small - more likely to incorrectly reject null

Question 11

testing autocorrelation

Answer 11

do regression of residuals et on their lagged values et-1

Question 12

HAC

Answer 12

Heteroscedasticity and Autocorrelation Consistent standard errors (they take autocorrelation into account)

Question 13

conditional heteroscedasticity

Answer 13

variance of the error term is autocorrelated (ie.e when it’s high in one period it’s high in the next
arises when dependent variable has volatility clustering

Question 14

AR(p) model

Answer 14

uses Yt-1 to forecast Yt. p = no. of lags

Question 15

AR(p) model assumptions

Answer 15

conditional expectation of ut = 0 given past values of Yt

errors are serially uncorrelated

Question 16

ADL(p,q) model

Answer 16

autoregressive distributed lag model
lagged values of dependent variable are included as regressors
p=lags of Yt, q=lags of additional predictor Xt

Question 17

least squares assumptions for ADL

Answer 17

error term has conditional mean 0 given all the lags of regressors
random variables have a stationary distribution
no large outliers
no multicollinearity

Question 18

stationarity

Answer 18

series Yt is stationary if its probability distribution doesn’t change over time

Question 19

types of non-stationary

Answer 19

trends and breaks

leads to bias an inconsistency

Question 20

deterministic trend

Answer 20

variable is a linear function of time (would indicate that growth rate is constant over time)

Question 21

stochastic trend

Answer 21

trend is random and varies over time (UK GDP growth rate is not constant)

Question 22

random walk

Answer 22

Yt = Yt-1 + ut

if Yt follows an AR(1) with B1=1 then Yt contains a stochastic trend and is non-stationary

Question 23

random walk with drift

Answer 23

Yt = B0 + Yt-1 + ut

Question 24

problems with stochastic trends

Answer 24

biased coeff estimates
non-normal distributions of t-stat
spurious regressions

Question 25

testing for a unit root

Answer 25

Dickey-Fuller test

Question 26

Dickey-Fuller test

Answer 26

regressing Yt on its lag testing for the existence of a stochastic trend in the presence of a deterministic trend (we include an intercept and a time trend into spec on unit root test)

Question 27

Augmented Dickey-Fuller test

Answer 27

if AR(1) model doesn't capture all the serial correlation in Yt then DF test is invalid

Question 28

differencing

Answer 28

eliminates stochastic trend | transforming non-stationary time series to stationary

Question 29

Chow test

Answer 29

to test fr breaks in ADL and DL models in a subset of parameters only

Question 30

BIC (lag selection)

Answer 30

Bayes Information Criteria - want to choose p that minimises BIC

Question 31

AIC (lag selection)

Answer 31

Akaike Information Criteria - want to choose p that minimises AIC

Question 32

SSR (p)

Answer 32

sum of squared residuals of a model estimated with p lags

Question 33

focus of forecasting

Answer 33

how good is a model at predicting future events (not to estimate causal effects)

Question 34

to evaluate forecasting model (and compare different models)

Answer 34

adjusted R^2 RMSFE out-of-sample forecasting performance

Question 35

RMSFE

Answer 35

the root mean squared forecast error = size of typical mistake we make when using forecasting model (smaller means better model)

Question 36

adjusted R^2

Answer 36

how well does the model explain the variation in the dependent variable (higher means explains more of variation)

Question 37

out-of sample forecasting performance

Answer 37

how well is the model performing in real time

Question 38

forecast errors

Answer 38

mistake made when forecasting (not the same as predicted residuals)

Question 39

pseudo out-of-sample forecasting

Answer 39

method for simulating real time performance of a fc model using historical data for the series Y up to period T

Question 40

standard deviation of pseudo out-of-sample forecast errors provide

Answer 40

estimate of RMSFE

Question 41

95% forecast interval

Answer 41

interval that contains the future value of the series 95% of the time

Question 42

Granger causality tests

Answer 42

tests of the predictive content of the predictors in a forecasting model stat = F-stat the predictor "Granger causes" w/e

Question 43

dynamic causal effect

Answer 43

follow time path of the effect of a shock over time e.g. effect of increasing IR on US GDP

Question 44

DL Model

Answer 44

distributed lag model - used to estimate dynamic effect

Question 45

DL model assumptions

Answer 45

exogeneity random variables have a stationary distribution no large outliers no multicollinearity

Question 46

exogeneity

Answer 46

condition that guarantees that the estimated coeffs can be interpreted as causal effects - will not hold if there are omitted variables in error term that are correlated with past or present values - holds if lags don't effect w/e beyond last lag