Study Session 3 - Time Series Analysis Flashcards
What is a time series? What is a trend? Types of Trend?
a set of observations for a variable over successive periods of time. Has a trend if you can see a pattern can be seen by plotting the data.
Only difference between this equation and simple regression is that Yt becomes data point from the time series to predict the next.
Linear or Log
Log convex - growth, concave - decay
How is the log exponential transformed to linear?
ln(yt)= ln(e^b₀+b₁(t)= ln(yt) = b₀+b₁(t) - can now be used in linear regression.
When do you use a linear trend model? Log-linear model?
When is appears the data points are equally above and below the regression line, use linear. If curved or persistently above or below the regression line then you log-linear. If it is growing at a constant rate use log-linear.
What do you use when log-linear is appropriate but exhibits serial correlation?
Autoregressive.
What is an autoregressive model?
When the dependent variable is regressed against one or more lagged values (previous periods) of itself.
Must be covariance stationary or inferences based on the model are not valid.
What are the three conditions for covariance stationary?
The expected value of the time series in constant over time. (mean reverting level).
The time series volatility around its mean doesn’t change over time.
The covariance of the time series with leading or lagged values of itself is constant.
Constant EXPECTED VALUE, VARIANCE, and COVARIANCE.
What is the chain rule of forecasting?
Because you are working with lagged values, you must calculate one step forward before two step forward, etc.
How do you test for serial correlation in an autoregressive model?
- Calculate the autocorrelations of the model’s residuals (the level of correlation between the errors - forecast v. actual, one period to the next)
- Test whether the autocorrelations are significantly different from zero using a t test where
t= correlation between 𝝴t, 𝝴t-k/ 1/√T
correlation between error term t and kth lagged error term.
df = T-2
What is mean reversion?
time series exhibits mean reversion if it has a tendency to move towards it’s mean. If we are at the mean reverting level, the next predicted value will be the same.
So if xt > larger than mean reverting level, next will be lower than xt and vice versa.
What is the formula for mean reversion?
xt= b₀/(1-b₁)
Difference between in-sample forecasts and out of sample forecasts?
In sample are within the range of the data (time period)
out of sample are made outside the range. Tests whether the model adequately describes the time series.
What is the root mean squared error criterion (RMSE)?
used to compare the accuracy of autoregressive models in forecasting out of sample values. Lower, better forecast.
What is instability of variables?
Also known as none stationary. Data can be dynamic, variables changing all the time.
What is a random walk? With constant drift?
the predicted value of the series in one period is equal to the value of a series in the previous period plus a random error term.
xt = xt-1 +𝝴t where the best forecast is t, t-1 and the expected value of each error term is zero, the variance is constant, and there is no serial correlation.
Constant drift increases or decreases the walk by the same amount each period. It’s an intercept. +/-
Why is a random walk not covariance stationary?
Must have a finite mean-reverting value.
xt = b0/0, not defined.
