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Time Series Analysis

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Whenever we have data recorded sequentially over time, and considered them to be on an important aspect of data have a?
time series
Are time series spaced at roughly regular intervals ?
Yes
What are the objective of most time series?
provide forecast of future values of the time series
What are the two types of forecasting?
What's the difference?
Qualitative: when historical data are unavailable
quantitative: when available
Two types of quantitative forecasting method?
Time series (extrapolation) and Causal (econometric)
involves forecasting future values based entirely on the past and present values of a variable
time series
involve the determination of factors that relate to the variable you are trying to forecast
causal (econometric)
What does time series assume?
that the factors that have influence activites in the past and present will continue to do so in approximately the same way in the future
What are the four components in time series models?
TISC
time is usually shown on the horizontal axis and the observed values on the vertical axis
time series plot
the value of the observation at time period t
y
denotes the number of historical observations of y
T
observations in this time series are equal
the base series
an overall long term upward or downward movement in a time series
trend
this constant per period change is then the slope of the linear trend line
linear trend
the percentage increase in Yt from period to period remains constant
exponential trend
Product life cycle
S shaped trend
Many time series have seasonal variation? T/F
True
typically seasonal components repeat annually, but the are a few exception?
24 hours
regular cycles in the data with period longer than one year are referred to as?
cyclical variation
What is hard to predict? cyclic or seasonal component why?
Cyclic variation because it's more irregular
What are the factors that determined time series?
Trend, seasonal, and cyclic components.
random variation explains unpredictable behaviors of human beings
represents random fluctuations in the data due to irregular or unpredictable events
random variation (noise)
The random variation components give most time series graphs their irregular, ____ appearance
zigzag
If noise increases in magnitude, what happens?
it makes it harder to distinguish the other components
many times-series follow a long term trend except for?
random variation
What are the three types of regression based trend models?
linear, quadratic, and exponential
time series models means that the time series variables changes by a constant amount each time period
linear trend
What's the linear trend model
Check
What is the linear trend forecasting equation?
Check
~The interpretation of b in a linear trend model?
~ If b is positive the trend is?
~ If b is negative the trend is?
the expected constant change in the time series from one period to the next
Upward
Downward
The interpretation of a in a linear trend model?
estimate the expected value of the time series at t = 0
Forecast for future time periods are made via ____
extrapolation
What are more appropriate? Prediction or confidence intervals?
prediction
What is the quadratic trend model?
Check
What is the quadratic trend forecasting equation?
Check
When the quadratic term is significant, the linear term is kept in the quadratic model even if it is not significant? T/F
True
When a time series change at a rate such that the percentage differences from value to value is constant
Exponential trend
Exponential trend model?
Check
~ How do you make the exponential trend model linear?
~ What is the equation?
By taking the logarithm
Check
If a time series exhibits an exponential trend, then a plot of its logarithm should be approximately _____?
linear
What is the exponential trend forecasting equation?
Check
How to find the y intercept in an exponential trend?
You take the antilog a and find the e^x.
How to find the slope coefficient in an exponential trend?
By expressing the b as a percentage
How come you can't use the standard error of the exponential trend?
because it's not in log format
What is the mean square error (MSE) equation?
Check
Do you want a large or a small MSE?
small
What is the root mean square error (RMSE)?
Check
What do you do when the value of MSE and RMSE becomes inflated through the squaring process?
By finding the Mean Absolute Error (MAE) or the Mean absolute deviation (MAD)
MAE equation?
Check
Do you want a small or a large MAE?
small
What is the MAPE equation?
Check
A model that makes any one of these errors measures small tends to make the other three small as well? T/F
True
When trying to find a forecast for time period T+1 we use the model called?
naive forecasting model
Unfortunately, the existence of random variation often makes the task of identifying the other three components (Long term, seasonal, cyclical variation) difficult, so we use which two most widely used smoothing techniques?
moving averages and exponetial smooth
The forecast for the next time period will be computed by dropping the oldest observation and adding in the newest?
moving average
Remember:
~ If L = n, then the entire data set would be used in the average.
~ If L = 1, we have the naive forecast Yt+1 = Yt
Okay
What happens to the moving averages as the length L increases?
The moving averages series with the greater length is smoother because a larger L cannot respond to rapid changes in a time series like a shorter L can
What length should be used?
If you are interested in long term behavior or have a series with random noise, use a longer moving average; however, if it's a short term change use a shorter moving average.
techniques base their forecast on a weighted average of past observations, with more weight on the more recent observations?
Exponential smoothing
The three most widely used methods for exponential smooth are?
Single, Double, Winter's method
It performs best when there is no pronounced trend or seasonality in the series
single (simple) exponential smoothing
Designed for cases when there is a trend in the data, but no seasonal variation
Double (Holt's method) exponential smoothing
Is is appropriate for a series with both trend and seasonal variation
Winters' method
What is a smoothing constant?
a (0<a<1)
Simple Exponential Smoothing
____ smoothing constants provide forecasts that respond slowly to changes in the series. ___ smoothing constants do the opposite
Small;large
Equation for smoothing constant?
check
What is a basic property of moving average forecasts?
the future forecasts tend to be close to the last few values of the series
The larger smoothing constant produces a less smooth forecast curve and?
The larger smoothing constant produces a less smooth forecast curve and slightly better error measures
True or false? The future forecast from simple exponential smoothing are always flat?
True
forecasting method intended to perform best when the time series to be forecast has a tend, but no seasonal component
Hold's method
Lt is?
the level of the series at time t
an estimate of the change in the series from one period to the next?
Tt (trend term)
The a and B in a Holt's method forecast is assumed to be between?
0 and 1
What does the zero smoothing constant for trend mean?
It doesn't mean that there is no trend, it means that the initial estimate of trend is kept throughout
~Often able to react quickly to a sudden upswing or downswing in the data.
~Typically has a delayed reaction to such a change.
Holt's method; Simple