Week 4 Flashcards
(28 cards)
How to choose alpha for exponential smoothing?
trade off between trusting xt when alpha is large and trusting s_t-1 when alpha is small.
More randomness - trust previous estimate S_t-1
Less randomness - trust what you see x_t
Time series complexities
Trends - increasing an decreasing
Cyclical patterns - Annual temp cycles, weekly sales cycles, daily blood pressure cycles
How to deal with cyclic patterns
Like trned- additive component of a forula
Multiplicative
Multiplicative
L: length of a cycle
C_t: the multiplicative seasonality factor for time t: Inflate or deflate the observation
If C is 1.1 on Sunday when sales were ____ higher just because it was a sunday
10%
If 550 sold on Sunday then 500 is baseline value and 50 is 10% extra
Starting condition for Trend in exponential smoothing
Trend: T1 = 0, shows no initial trend
Multiplicative seasonality
ultiplying by 1
shows no initial cyclic effect
First L values of C set to 1
Triple exponential smoothing is called
WInter’s method or Holt - WInters
In exponential smoothing, more recent observations or ore important . T F
T. Newer observations are weighted more
Forecasting with trend
The best estiate of the next baseline is the most current baseline estimate
The best estimate of the trend is the most current trend estimate
How to find good values of alpha, beta , and gamma
Optimization. Minimize sum of squared error across dataset
ARIMA
Autoregressive integrated moving average(ARIMA)
Three key parts to ARIMA
1) DIfferences: Sometimes differences in data can be stationary
2) Auto regression: Predicting current value based on previous time periods
3) Moving average: Previous errors as predictors
Stationary process
if the mean, variance, and other measures are expected to be constant over time
Regression
predicting the value based on other factors
auto
using earlier values to predict
This only works with time series data
ARIMA combines autoregression and differencing
autogression on the differences
use p time periosds of previous observations to predict dth order differences
ARMIMA(0,0,0)
white noise
ARIMA(0,1,0)
Random walk
ARIMA(p,0,0)
AR Model
ARIMA(0,0,q)
Moving average model
ARIMA(0,1,1)
basic exponential smoothing model
WHen does ARIMA work better than exponential smoothing
When data is stable with fewer peaks valleys and outliers
How many past data points do you need for ARIMA to work well?
40
GARCH
Generalized Autoregressive Conditional Heteroscedasticity
Estimate or forecast variance of something for which we have time series data
