Analysis of Sequential Data
MSE Module TSM_AnSeqDa
MSE Module TSM_AnSeqDa
Set of flashcards Details
| Flashcards | 96 |
|---|---|
| Language | Deutsch |
| Category | Maths |
| Level | University |
| Created / Updated | 17.01.2021 / 08.09.2023 |
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Which nise properties need to be checked?
- We estimate the properties of the noise from the residual of the models
- We need to check the residuals to be unbiased, in order to assume the mean of the noise to be 0
- We need to check that the residuals are uncorrelated in order to use the summation of the variance of the noise at vasious time steps
- We estimate the variance of the noise to be equal to the variance of the residuals
- Once checked the assumptions about the residuals, we can conpute the prediction intervals
Predict yt+2 (and 95% prediction interval) of the following example:
Predict yt+4 and the 85& prediction interval of the following example:
What are the most important percentiles of the normal distribution and for which confidence level are they used?
How looks the forecast equation of Simple Exponential Smoothing (ses)?
How looks the weighted average form of the forecast equation of simple exponential smoothing (ses)?
How would you advance the following example with simple exponential smoothing?
What is the Holt's linear trend in simple exponential smoothing about? Name its forecast, level and trend component:
What is the Damped trend method in simple exponential smoothing (ses) about? Name the forecast, level and slope component. What are the parameters and how do you estimate them?
- Parameters
- Alpha, beta, b, l, fi
- How to estimate
- Optimize over sum of squared estimate of errors (SSE)
Solve the following exercise:
At t=0:
- level: l0 = 445
- Slope (trend): b0 = 9
- We call fitted value the one-step predictions made on the training set, for which it is possible computing the residual
- fitted value:
- y[hat]1 = l0+b0 = 445+9 = 454
What does time series decomposition mean? In which components can you decompose the time serie at each time step?
Solve the following example with the simple exponential smoothing (ses) model:
Solve the following example with the simple exponential smoothing (ses) with trend model:
Solve the following example with the simple exponential smoothing (ses) with damped trend model:
How do you choose between competing model?
- Selecting the model with lowest sum of squared residuals (sse) would lead to overfitting
- Statistical model selection: Select the model which maximizes a score composed by the log likelihood ( proportional to the sum of squared residuals) and a penalty related to the number of parameters in the model --> AIC
- More complex models have in general lower residuals but higher number of parameters (higher penalization)
What is the AIC about?
- Statistical model selection: Select the model which maximizes a score composed by the log likelihood ( proportional to the sum of squared residuals) and a penalty related to the number of parameters in the model --> AIC
What is the letter k in AIC for and how do you set it for ses, ses with trend, ses with damped trend?
- k is the total number of parameters and initial states that have been estimated, including the variance of the residuals
- ses: k=3 (l0, alpha, sigma)
- ses with trend: k=5 (l0, alpha, sigma, b, beta)
- ses with damped trend: k=6 (l0, alpha, sigma, b, beta, fi)
How are the two seasonal forecasting method called?
- Holt-Winters additive method
- to capture seasonality
- Holt-Winters multiplicative method
- for when seasonal variations are changing proportional to the level of the series
How looks the Howt-Winters additive method?
How looks the Holt-Winters multiplicative method?
What is often the single most accurate forecasting method for seasonal data?
How many parameters need to be estimated for the seasonal methods?
- Estimation of m+5 paramters
- 3 smoothing coefficients (alpha, beta, gamma)
- m+2 initial states (s1, ...., sm, l0, b0)
Calculate the fitted value Q1Y1 and Q2Y1 of the following example:
What is the taxonomy for the exponential smoothing methods?
We should be able to understand the table in the answers here. Really possible exam question: Write down the equation from <any model>.
How are the R commands performed to use the exponential smoothing methods?
When are additive and when are multiplicative seasonality models chosen?
What is the relation between the prediction interval of simple exponential smoothind and the naive model?
Look at the prediction interval exercises for the ses model!
LOOK AT IT! ;)
What are the innovations state space models, what is their abbreviation and what is the difference to the exponential smoothing methods?
- Innovations state space models (Error, Trend, Seasonal: ETS)
- Generate same point forecasts as ses but can also generate forecast intervals
- A stochastic (or random) data generating process that can generate an entire forecast distribution
- Allow for "proper" model selection
- Exponential smoothing methods
- Algorithms that return point forecasts
How work the ETS models?
- Each model has an observation equation and transition equations, one for each state (level, trend, seasonal), i.e. state space models
- Two models for each method: one with additive and one with multiplicative errors, i.e., in total 18 models
- ETS(Error, Trend, Seasonal)
- Error = {A,M}
- Trend = {N,A,Ad}
- Seasonal = {N,A,M}
How are the forecast errors in ses models calculated?
How looks the ETS(A,N,N) model?
How look the ETS(A,A,N) model?
How looks the ETS(A,A,A) model?
How looks the ETS(M,N,N) model?
How looks the ETS(M,A,N) model?
Look ate the additive error ets models equations:
Look at the multiplicative error ets models equatoins:
How are ets models estimated and on which accuracy metric?
