midterm 3 Flashcards
temporal ordering
past values can influence future values, but not vice versa. In time series analysis, this distinguishes it from cross-sectional data.
data frequency
the interval at which data points are collected: annual, quarterly, monthly, daily
static model
a regression mode where the effect of the explanatory variable Z on the dependent one is immediate, with no lagged effects.
yt=beta0 + beta1Zt + ut
finite distributed lag model FDL
a regression model that includes both current and lagged values of an explanatory variable to capture delayed effect
yt = alfa0 + delta0Zt + delta1Zt-1 + ut
order of FDL
the number of lagged values of the explanatory variable included in an FDL model.
if its 2 it means Zt, Zt-1, Z-2
impact propensity/ impact multiplier
the immediate effect of a one-unit change in the explanatory variable Z on the dependant variable
long-run propensity
the total cumulative effect of a permanent one-unit change in Z on y over time
trending time series
a time series that shows a consistent upward or downward movement over time. like GDP
spurious regression
occurs when we ignore a trend, and suggest a relationship when there is none. Leads to biased estimation. Affect both the dependent and independent. Adding the appropriate time trend eliminates the problem
linear trend
steady increase or decrease
trendt= alfa0 + alfa1t
quadratic trend
u shaped, accelerating or decelerating
trend= alfa0 + alfa1t + alfa2t”2
exponential trend
rapid (%) growth
trendt= alfa0e”alfa1t
detrended variables
removing long-term trends tp focus on short-term variations. Helps avoid spurious regression result.
hump-shaped (inverted u shape) trend
a trend where a variable initially increases, reaches a peak and then decreases.
u shaped trend
a trend where a variable decrease initially, hits a min, and then increases
quarterly data
time series data collected every 3 months
seasonality
recurring patterns in a time series tied to specific times of the year
deseasonalised data
data adjusted to remove seasonal effects, making it easier to analyse trends and other factors. extending the model with seasonal dummies
seasonally adjusted data
similar to deseasonalised data, but explicitly adjust to remove both upward and downward seasonal fluctuations.
seasonal dummies
binary variables representing specific seasons in regression models. D1, D2, D3, D4 one of them is the based season
base/benchmark season
the omitted season when using seasonal dummies. All the other seasonal effects are interpreted relative to this base season
contrast variable
alternative to seasonal dummies to avoid the dummy variable trap (perfect collinearity). Express the difference between seasons instead of using absolute levels.
standardised OLS coefficient (regression)
its obtained after standardising all the variables. Involves converting variables to have a mean of 0 and a standard deviation of 1. This makes the coefficient scale-independent, allowing comparison across variables with different units of measurement
relative importance measure
the higher the absolute value of the standard OLS coef. the more important is the particular regressor in terms of dependant var.
stochastic time series analysis
studies time series with inherent randomness, focusing on autoregressive (past levels affect the present) and moving average (learning from the error terms in the past) structure. Appropriate only for short-term forecasting. The series must be stable/stationary
self-generative structure
the present value is influenced by its own past values and past shocks or errors.
autoregressive process (AR)
the current value (yt) depends on its previous values (yt-1) and a random error term (ut)
p lag
moving average process (MA)
the current value is influenced by the past errors term (ut-1)
q lag
ARMA (p,q) model
combines AR and MA components into a single model
ARIMA (p,i,q)
extends the ARMA model to handle non-stationary processes by differencing the data i times to achieve stationarity
p: order of AR
i: number of differences
q: order of MA
stationary/stable time series
a time series is stationary if its mean, variance and autocovariance do not change over time
autocovariance
the covariance betwen 2 values of the time series separated by k time units
autocorrelation function ACF
measures the correlation between yt ( immediate influence) and yt-k (indirect)
partial autocorrelation function PACF
measures the direct effect between values, removing the indirect effect (intermediates)
correlogram
graph showing ACF and PACF for different lags
white noise
constant expected value and constant variance whose subsequents are uncorrelated and independent.
random series with constant mean and variance, uncorrelated errors.
no autocorrelation exists between observations
ljung-box test
test if residuals are white noise.
H0: no autocorrelation, white noise
H1: there is at least 1 autocorrelation
random walk
AR (1) process with unit root, nonstationary, xero constant.
Current value depend solely on the previous value + a random error.
ACF not collapsing to zero
unit root process
non stationary, shocks persist indefinitely
trend stationary process
stabilised by removing a deterministic trend. Turning it into a stationary
difference stationary process
a non stationary, but can be made stationary by taking the first ( higher order) differences, meaning differencing
augment dickey-fuller test
to determine if a time series has unit root, by adressing potential autocorrelation in the residual. Add a lagged difference of the dependent ( d_yt)
problem: the lag order (p) is unknown and has to be determined somehow.
unit root test
checks stationarity by testing for unit roots
box-jenkins algorithm
for ARIMA
step1: check the stability of the process
step2: id needed, stabilise the time series with appropriate transformation (detrending= -trend; differencing)
step3: determine the (p;q) orders for the ARIMA model and run the estimation on the transformed stationary data (akaike, or z test)
step4: model diagnostics, the residual must be WN (correlogram, ljung-box test)
step5: forecast future out of sample values of the time series = invert all the transformations which were previously applied
integrated process I(i)
a series that becomes stationary after i differences
