Time Series : Basics Flashcards
Give the definition of a time series and some examples.
Definition : A time series is a series of observations y1, y2, ... yt over consecutive tie periods, such as months or years. Examples: . Daily stock prices . Volume of stock trades, by day . Monthly sales
What is the goal of a time series analysis?
Finding patterns that can help predict future values. The patterns may relate the term yt to previous terms or to the time variable t.
What is longitudinal data?
Data from a process that varies with time
What is cross-sectional data?
Data that is not organisez by time
What is a causal model?
A regression model in which a dependent variable is a function of explanatory variables OTHER than time.
Time series can be decomposed into three parts. Name those three parts.
. Trend
. Seasonal factors
. Random patterns
Define the trend
long-term pattern of the data
Define seasonality
cyclical pattern of the data
What is a time series plot?
Scatter plot of a time series against time with the consecutive points connected with lines
What are two shortcomings of regression models for time series?
- they are naive : they ignore information other than time series being modeled
- they give the highest weight to the earliest and latest observations (the ones with t furthest away from the mean).
Why is they giving the highest weight to the earliest and latest observations a shortcoming?
When forecasting, you want to give the highest weight to the latest forecast and the lower weight to the earliest forecast.
What does it mean when a time series is “stationary in the mean” and how can you estimate the mean?
The mean does not vary by t.
The mean can be estimated as the sample mean of the observed values
What does it mean when a time series is “stationary in the variance” and how can you estimate the variance?
The variance does not vary by t.
The variance can be estimated as the sample variance of the observed values
True or false : time series terms are not correlated with each other.
FALSE : Time series terms tend to be correlated with each other.
Why is the true variance underestimated in a time series?
Because time series terms tend to be correlated with each other. However, the bias reduces rapidly as the size of the series increase.
What is the autocorrelation?
Correlation of a time series with itself.
What is the lag?
The distance between the term yt and y(t+k)
What are the characteristics of a time series that is (weekly) stationary?
Stationary in the mean and variance and autocorrelation is a function only of the lag and NOT of the time
The higher moments of the series may still vary with time
What are the characteristics of a time series that is (
strongly stationary?
None of the moments of the time series can vary with time
What is the sample autocorrelation at lag 0?
1
What is a white noise time series?
A time series in which each term is independent and has constant mean and constant variance. We usually assume that the terms are normally distributed.
Why are the autocorrelations at all lags greater than 0 equal to 0 in a white noise time series?
Because the terms are independent.
What is the l-period look-ahead forecast of a white noise time series?
The sample mean of the observations (y barre)
True or false: the width of the forecast interval is independent of l in a l-period look-ahead forecast of a white noise time series?
True
What is a filter?
The procedure for reducing a time series to white noise.
Explain the process of a filter?
We try to reduce any time series to white noise by finding patterns, leaving the unexplained part as white noise
How do we call the uncertainty that cannot be explained by patterns in a time series?
Irreductible
How can you identify a time series?
If the series has more or less constant mean and variance and doesn’t move around much.
What is a random walk?
A nonstationary time series which is the initial level “y0” plus the accumulation of white noise (ct)
It a random walk still nonstationary is the mean of the white noise ( E[ct] ) = 0 ?
Yes because the variance of a random walk increases with time
What is called E[ct] ?
“drift”
What is called a random walk where E[ct] =/=0 ?
Random walk with drift.
What are the differences of a random walk?
White noise
How can you identify a random walk?
- Check the patterns of the values : for a RW, the values increase at a constant rate and the variance is a linear function of time
- Differencing the time series should result in white noise (the pattern of value should be constant with constant variance over time)
- Std of differences should be significantly lower than std of initial series
What is the difference of a linear trend in time and a random walk?
A linear trend has stationary variance, whereas a rw’s variance increases with time.
What is the error term of a linear trend in time?
White noise making it stationary
What is the error term of a random walk with drift?
Random walk making it nonstationary
What are two filtering methods?
- Differencing a random walk
2. Taking the logarithm of a time series to stabilise its variance
What is a control chart and what are the UCL and LCL?
Chart upon which control limits are superimposed.
UCL = (ybarre) + 3 (sy)
LCL = (ybarre) - 3 (sy)
Give examples of control charts for time series
- Xbarre charts : calculate the averages of series of k observations. The variance of an average is lower than the variance of the series so unusual patterns should stick out
- R charts : calculate the range of series of k observations (maximum observation - minimum observation). The range is a simple measure of variability and the chart helps evaluate patterns.
How do you evaluate a forecast?
Out-of-sample validating technique.
Split the data in two groups. Use de data up to time T1
What statistics can be used to evaluate a forecasting model (based on error term)?
- Mean error statistics
- Mean percentage error
- Mean square error
- Mean absolute error
- Mean absolute percentage error
Which statistics will reveal trend patterns but won’t reveal problems when the residuals are positive and negative but have a low average?
ME and MPE
Which statistic can’t be used if the series has 0s and may not be logical if the series have negative terms?
MPE
Which statistic can’t be used if the error terms have 0s or may not be logical if the error terms are negative?
MAPE
True or false : for quality measures for validation of models, the higher the value, the better.
False, the smaller the better
