Time series forecasting arma arima sarima

1. Time Series Forecasting

2. A Time Series
Is a sequential set of data points,
measured typically over
successive times.

3. Example

4. Time Series
Univariate
A time series
containing records
of a single variable.
Multivariate
A time series
containing records of
more than one variable.

5. Time Series
Continuous
Observations
measured at every
instance of time.
Discrete
Observations
measured at discrete
points of time.

6. Example

7. Components of a Time Series
◉ Trend.
◉ Cyclical variations.
◉ Seasonal variations.
◉ Irregular variations.

8. Trend
The general tendency of a time series to increase,
decrease or stagnate over a long period of time.
1

9. Example

10. Cyclical variation
Changes in the series, caused by circumstances,
which repeat in cycles.
2

11. Example

12. Seasonal variations
Fluctuations within a year during the season.
3

13. Example

14. Irregular or random variations
Caused by unpredictable influences, which are
not regular and also do not repeat in a particular
pattern.
4

15. Example

16. “Time Series Analysis
The procedure of fitting a
time series to a proper model.

17. “Concept of Stationarity
The statistical properties such as
mean and variance of a stationary
process do not depend upon time.

18. “

19. “

20. “Time series Stationarity is a
necessary condition for building a
time series model that is useful for
future forecasting.

21. Time Series Forecasting Models
◉ Stochastic Models.
◉ ANN-based Models.
◉ SVM-based Models.

22. Time series forecasting using Stochastic Models
◉ Auto-Regressive Model.
◉ Moving Average Model.
◉ ARMA Model.
◉ ARIMA Model.
◉ SARIMA Model.

23. Auto-Regressive ModelDITS
AR(p)
The feature value of a variable is assumed to be a
linear combination of p past observations.

24. Auto-Regressive ModelDITS
AR(1)
𝑋(𝑡) = 𝑎 ∗ 𝑋(𝑡 − 1) + 𝑤

25. Auto-Regressive ModelDITS
Linear Regression

26. ARMA Model
𝐴𝑅𝑀𝐴(𝑝, 𝑞)
Combination of Two Models
AR(p)
MA(q)

27. ARMA Model
Stationarity

28. ARIMA Model
Ordinary differencing
𝐴𝑅𝐼𝑀𝐴(𝑝, 𝑑, 𝑞)

29. ARIMA Model
𝑦𝑡
(1)
= 𝑦𝑡 − 𝑦𝑡−1

30. ARIMA Model

31. ARIMA Model

32. SARIMA Model
𝑆𝑒𝑎𝑠𝑜𝑛𝑎𝑙 𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑖𝑛𝑔
𝑦𝑡
(1)
= 𝑦𝑡 − 𝑦𝑡−𝑠

33. SARIMA Model

34. SARIMA Model

35. SARIMA Model

36. Time series forecasting using ANNs
◉ Universal functional approximators.
◉ Solve Nonlinear problems.
◉ Data Driven.
◉ Generalization.
◉ Tolerate noise in data.

37. Time series forecasting using ANNs

38. Time series forecasting using ANNs

39. Time series forecasting using SVM
◉ Function Approximation.
◉ Good Generalization.
◉ Optimal Separating Hyperplane.
◉ Regression Problems.
◉ Time Series Predication.

40. Time series forecasting using SVM

41. Comparison - Example

42. Comparison - Example
 Observed
 Stochastic
 ANN
 SVM

43. THANKS!

44. https://www.shamra.sy/academia/show/5b0c09997726f
Research URL