Time Series Model Building Process - Revision history

Hazn00: /* Conclusion */

2020-01-20T18:14:48Z

‎Conclusion

2020-01-20T18:14:06Z

‎{\phi}_1 = 0.0 and {\phi}_2 = 0.9

2020-01-19T14:38:39Z

‎Conclusion

2020-01-19T14:38:24Z

‎Conclusion

2020-01-19T14:15:44Z

‎Simulation

2020-01-19T14:14:57Z

‎Models.py

2020-01-19T14:10:04Z

‎Data Generating Process

2020-01-19T14:08:29Z

‎Results

2020-01-19T13:58:05Z

‎Results

2020-01-19T13:55:38Z

‎Results

@@ Line 87: / Line 87: @@
 ===<math>{\phi}_1 = 0.0</math>  and <math>{\phi}_2 = 0.9</math>===
 BIC is the best method for small and big samples again.
-As we can see, Spec-to-gen method gives us very wrong in approximately 1/4 cases, because the null value gives no sense in this case.
+As we can see, Spec-to-gen method gives us very wrong result in approximately 1/4 cases, because the null value gives no sense in this case.
 ===<math>{\phi}_1 = 0.4</math> and <math>{\phi}_2 = 0.4</math>===

@@ Line 87: / Line 87: @@
 ===<math>{\phi}_1 = 0.0</math>  and <math>{\phi}_2 = 0.9</math>===
 BIC is the best method for small and big samples again.
-We never want to use the Spec-to-gen method, because
+As we can see, Spec-to-gen method gives us very wrong in approximately 1/4 cases, because the null value gives no sense in this case.
 ===<math>{\phi}_1 = 0.4</math> and <math>{\phi}_2 = 0.4</math>===

@@ Line 81: / Line 81: @@
 Previous periods don't have big impact.
 AIC method works well with smaller  samples. In case of bigger samples, BIC method works better than AIC.
 ===<math>{\phi} = 0.9</math>===

← Older revision		Revision as of 14:38, 19 January 2020
Line 78:		Line 78:

	== Conclusion ==		== Conclusion ==
		+	===<math>{\phi} = 0.1</math>===
		+	Previous periods don't have big impact.
		+	AIC method works well with smaller samples. In case of bigger samples, BIC method works better than AIC.
		+
		+
		+	===<math>{\phi} = 0.9</math>===
		+	BIC is the best method for small and big samples. Even though the GETS method doesn't work quite well, it is commonly used. The bigger tha max value of p is used, the bigger is the probability of getting the wrong guess from the simulation.
		+
		+	===<math>{\phi}_1 = 0.0</math> and <math>{\phi}_2 = 0.9</math>===
		+	BIC is the best method for small and big samples again.
		+	We never want to use the Spec-to-gen method, because
		+
		+	===<math>{\phi}_1 = 0.4</math> and <math>{\phi}_2 = 0.4</math>===
		+	This process is set to not be influenced by previous periods.
		+	The BIC method works the best again.

	== Code ==		== Code ==

@@ Line 62: / Line 62: @@
 === Simulation ===
-Perform n Monte Carlo simulations, where in each simulation a the data generating process is used to create a time series. Then the AR(p) model is estimated for ''p=0,1,…,pmax'', and the best models are selected according to the selection criteria described above. Therefore, we will obtain four estimates of p that corresponds to the described methods for each of the n simulation. The final step is to compute % success of correctly estimated p for each of four methods.
+Perform n Monte Carlo simulations, where in each simulation the data generating process is used to create a time series. Then the AR(p) model is estimated for ''p=0,1,…,pmax'', and the best models are selected according to the selection criteria described above. Therefore, we will obtain four estimates of p that corresponds to the described methods for each of the n simulation. The final step is to compute % success of correctly estimated p for each of four methods.
 == Controls ==

@@ Line 81: / Line 81: @@
 == Code ==
 === Models.py ===
 <pre>
 import numpy as np from numpy.linalg

@@ Line 46: / Line 46: @@
 === Data Generating Process ===
-To answer the question, which model selection method is the best, we are creating an artificial data. We assume that data are created by AR(1) process
+To answer the question, which model selection method is the best, we are generating an artificial data. We assume that data are created by AR(1) process
 <math>x_t = {\mu} + {\phi}_1x_{t-1} + {\epsilon}_{t'}</math>

@@ Line 74: / Line 74: @@
 File:Phi09.png|<math>{\Phi} = 0.9</math>
 File:Phi04Phi04.png|<math>{\Phi}_1= 0.4, {\Phi}_2 = 0.4</math>
-File:Phi04Phi04.png|<math>{\Phi}_1= 0.0, {\Phi}_2 = 0.9</math>
+File:Phi00Phi09.png|<math>{\Phi}_1= 0.0, {\Phi}_2 = 0.9</math>
 </gallery>

@@ Line 71: / Line 71: @@
 == Results ==
 <gallery>
-File:Phi01.png|Phi = 0.1
+File:Phi01.png|<math>{\Phi} = 0.1</math>
-File:Phi09.png|Phi = 0.9
+File:Phi09.png|<math>{\Phi} = 0.9</math>
-File:Phi04Phi04.png|Phi1 = 0.4, Phi2 = 0.4
+File:Phi04Phi04.png|<math>{\Phi}_1= 0.4, {\Phi}_2 = 0.4</math>
-File:Phi04Phi04.png|Phi1 = 0.0, Phi2 = 0.9
+File:Phi04Phi04.png|<math>{\Phi}_1= 0.0, {\Phi}_2 = 0.9</math>
 </gallery>