Chapter 17 Flashcards
Define Time Series
a sequence of observations on a variable measured at successive points in time or over successive periods of time
Define Measurements
can be: Hourly, daily, weekly, monthly, yearly or at any other regular interval
Define Pattern of the data
- important factor in understanding how the time series has behaved in the past
- if such behavior can be expected in the future, we can use this past pattern to guide us in selecting an appropriate forecasting model
What is the first step in forecasting
- construct a time series plot
Describe a timeseries plot
- graphical presentation of the relationship b/w time and the time series variable
- time on horizontal axis and time series on the vertical
What are some common types of data patterns
- Horizontal pattern
- Trend Pattern
- Seasonal Pattern
- Trend and seasonal pattern
- Cyclical pattern
Describe Horizontal Pattern
data fluctuates around a constant mean
What is stationary series
used to denote a time series who statistical properties are INDEPENDENT of time
It means that
- the process generating the data has a constant mean
- the variability of the time series is constant over time
- always have a horizontal pattern
Is simply observing a horizontal patter enough to conclude that the time series is stationary?
no
What is a trend pattern
- a time series pattern may also show gradual shifts of movement to relatively higher or low values over a longer period of time
What can cause trend pattern
- usually due to population increases or decreases
- changes in demographic characteristics of the population
- technology, and / or consumer preferences
What are exponential relationships
are appropriate when the % change from one period to the next is relatively constant
What is seasonal patterns
- seeing the same repeating patterns over successive periods of time
- ex. Pool co. expects lower sales in fall and winter months Peak sales in spring and summer
Do seasonal influences indicate any long term trend?
no
what is Trend and seasonal pattern
- combination of a trend and seasonal pattern
- need a forecasting method that has the capabilities of dealign with both trend and seasonality
what is cyclical pattern
an alternating sequence of points below and above the trend line lasting more than one year
- 0ften the cyclical component is due to multi-year business cycles
What is important to note about cyclical patterns
business cycles are extremely difficult if not impossible to forecast
- as a result, cyclical effects are often combined with long-term trend effects and called trend-cycle effects
What are the Methods for forecasting
- Time series 2. Casual method
What can forecasting methods be?
- Qualitative - Judgement
2. Quantitative
What is needed for quantitative forecasting
- past info about the variable being forecasted is available
- the info can be quantified
- it is reasonable to assume the pattern of the past will continue
What is time series forecasting
- historical data restricted to past values
2. based solely on past values and or past forecast errors
What is the objective to time series
discover a pattern in historical data or time series
What is the objective to time series
discover a pattern in historical data or time series
What kinds of quantitative forecasting methods are there
- Naive
- Moving average
- weight moving average
- exponential smoothing
What is the simplest forecasting method
Naive
What is the forecast error
Forecast error = actual value - forecast
How do you perform Naïve method
use the previous period to forecast the next
If the forecast error is positive what can we say
the forecasting method overestimated the actual value forecasted
if the forecasting error is negative what can we say
the forecasting model underestimated the actual value forecasted
What are the Measures of Accuracy
- MAE
- MSE
- MAPE
What is the formula for MAE
avg. of absolute value of forecast errors (absolute (positive only) forecast errors / n
What is the formula for MSE
MSE = Avg of the sum of the squared forecast errors
forecast errors / n-1
What is the formula for MAPE
MAPE = Forecast error / actual x 100
What does MAE stand for
Absolute Mean Error
What does MSE stand for
Mean Squared Error
What does MAPE stand for
The Mean Absolute Percent Error
What is MAE useful for
this measure avoids the problems of positive and negative forecast errors offsetting one another
What is MSE useful for
this measure also avoids the problem of negative and positive forecast errors offsetting each other
FOr every measure, what provides more accurate forecast than using the most recent observations as the forecast for the next period
the average of historical values
if the underlying time series is stationary, the average of all historical data will
always provide the best results
What if the underlying time series is NOT stationary? Why could that be?
could be due to changes in business conditions (ie contract for certain amount) can often result in a time series that has a horizontal pattern shifting to a new level
- this would take a long time for the forecasting that uses the avg of all historical data to adjust
- in this case, the simple naive method adjusts very rapidly b/c it uses the most recent data
Which method adjusts rapidly
Naive method because it uses the most recent data
Describe the Weighted Moving average Method
each observation in the average calculation receives the same weight
Describe the variation called weighted moving average
select a different weight for each data value and then compute a weighted average of the most recent k values as the forecast
- most cases the most recent observations received the most weight, then the weight decreases for remaining older data values
- the sum of the weights = 1
ie. 3/6 - most recent
2/6 - second most recent
1/6 - the 3rd most recent
if we think that the recent past is a better predictor of the future than the distant past what should we do with the weighted average
larger weights s/b given to the more recent observations
What if the time series is highly variable ( in weight average)
- selecting approx equal weights is best
- only requirement is that the weights add up to 1
What can we use to determine whether one particular combination of data values and weights provides a more accurate forecast form another
use MSE as the measure of accuracy
- use the combination of # of data values and weights that minimizes MSE
What is exponential smoothing
- also uses weighted average
- se select only one weight - the weight for the most recent observation
- weights for the rest are computed automatically
- become smaller weights the further away
What is the formula for exponential smoothing
Ft+1 = aYt + (1-a)Ft
what is Ft+1
forecast of the time series for period t +1
what is Yt
actual value of the time series in period t
What is Ft
forecast of the time series for period t
what is a
alpha = smoothing constant (form 0 to 1)
Which methods adapt well to to changes in the level of a horizontal pattern
- moving averages
- weighted moving averages
- Exponential smoothing
When are moving average, weighted average and exponential not appropirate for
without modifications, not appropriate when significant tend, cyclical or seasonal effects are present
What is the objective to moving average, weight average and exponential smoothing
to “smooth out” the random fluctuations
- called smoothing methods
- easy to use
- provide a high level of accuracy for short range forecasts (ie next period)
When do you use Exponential smoothing method
used when we have no particular pattern, no seasonal variation, no weekly variation, just a series of numbers
- make a forecast based on the previous result and then correct it by how much the previous one was out
What are the exponential smoothing models
add
If the time series contains substantial random variability what can you use and why
a small value of the smoothing constant a is preferred
- b/c if much of the forecast error is due to random variability, we do not want to overreact and adjust too quickly
What do Larger values of a provide
the advantage of quickly adjusting the forecast
- react more quickly to changing conditions
How do you determine a desirable value for a
- choose a value for a that minimizes MSE
What is the linear trend equation
Tt = bo + b1t
What does Holt’s linear exponential smoothing do
forecast a time series with a linear trend
- uses two smoothing constants, a and B
- has 3 equations
What is non-linear trend regression used for
a series that have a curvilinear or nonlinear trend
What is the formula for non-linear trend regression
Tt = b0+b1t + b2t squared
What is the exponential trend equation used for
another alternative that can be used to model the non-linear pattern
What is the formula for exponential trend
Tt = b0(b1)exponent t
