# linear Gaussian state space model - local level model with seasonality and exogenous variables
# clear environment
rm(list=ls())
# UK car accidents data
data("Seatbelts")
help("Seatbelts")
library(KFAS)
## Warning: package 'KFAS' was built under R version 3.2.4
# define state-space model - local level with seasonality and two variables
y.SSM <- SSModel(log(drivers) ~
SSMtrend(1, Q=list(NA)) +
SSMseasonal(period=12,sea.type='dummy',Q=NA) +
log(PetrolPrice) +
law,
data=Seatbelts, H=NA)
y.SSM
## Call:
## SSModel(formula = log(drivers) ~ SSMtrend(1, Q = list(NA)) +
## SSMseasonal(period = 12, sea.type = "dummy", Q = NA) + log(PetrolPrice) +
## law, data = Seatbelts, H = NA)
##
## State space model object of class SSModel
##
## Dimensions:
## [1] Number of time points: 192
## [1] Number of time series: 1
## [1] Number of disturbances: 2
## [1] Number of states: 14
## Names of the states:
## [1] log(PetrolPrice) law level
## [4] sea_dummy1 sea_dummy2 sea_dummy3
## [7] sea_dummy4 sea_dummy5 sea_dummy6
## [10] sea_dummy7 sea_dummy8 sea_dummy9
## [13] sea_dummy10 sea_dummy11
## Distributions of the time series:
## [1] gaussian
##
## Object is a valid object of class SSModel.
# examine state
y.SSM$a
## [,1]
## log(PetrolPrice) 0
## law 0
## level 0
## sea_dummy1 0
## sea_dummy2 0
## sea_dummy3 0
## sea_dummy4 0
## sea_dummy5 0
## sea_dummy6 0
## sea_dummy7 0
## sea_dummy8 0
## sea_dummy9 0
## sea_dummy10 0
## sea_dummy11 0
# examine system matrices
y.SSM$T
## , , 1
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2
## log(PetrolPrice) 1 0 0 0 0
## law 0 1 0 0 0
## level 0 0 1 0 0
## sea_dummy1 0 0 0 -1 -1
## sea_dummy2 0 0 0 1 0
## sea_dummy3 0 0 0 0 1
## sea_dummy4 0 0 0 0 0
## sea_dummy5 0 0 0 0 0
## sea_dummy6 0 0 0 0 0
## sea_dummy7 0 0 0 0 0
## sea_dummy8 0 0 0 0 0
## sea_dummy9 0 0 0 0 0
## sea_dummy10 0 0 0 0 0
## sea_dummy11 0 0 0 0 0
## sea_dummy3 sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7
## log(PetrolPrice) 0 0 0 0 0
## law 0 0 0 0 0
## level 0 0 0 0 0
## sea_dummy1 -1 -1 -1 -1 -1
## sea_dummy2 0 0 0 0 0
## sea_dummy3 0 0 0 0 0
## sea_dummy4 1 0 0 0 0
## sea_dummy5 0 1 0 0 0
## sea_dummy6 0 0 1 0 0
## sea_dummy7 0 0 0 1 0
## sea_dummy8 0 0 0 0 1
## sea_dummy9 0 0 0 0 0
## sea_dummy10 0 0 0 0 0
## sea_dummy11 0 0 0 0 0
## sea_dummy8 sea_dummy9 sea_dummy10 sea_dummy11
## log(PetrolPrice) 0 0 0 0
## law 0 0 0 0
## level 0 0 0 0
## sea_dummy1 -1 -1 -1 -1
## sea_dummy2 0 0 0 0
## sea_dummy3 0 0 0 0
## sea_dummy4 0 0 0 0
## sea_dummy5 0 0 0 0
## sea_dummy6 0 0 0 0
## sea_dummy7 0 0 0 0
## sea_dummy8 0 0 0 0
## sea_dummy9 1 0 0 0
## sea_dummy10 0 1 0 0
## sea_dummy11 0 0 1 0
y.SSM$R
## , , 1
##
## [,1] [,2]
## log(PetrolPrice) 0 0
## law 0 0
## level 1 0
## sea_dummy1 0 1
## sea_dummy2 0 0
## sea_dummy3 0 0
## sea_dummy4 0 0
## sea_dummy5 0 0
## sea_dummy6 0 0
## sea_dummy7 0 0
## sea_dummy8 0 0
## sea_dummy9 0 0
## sea_dummy10 0 0
## sea_dummy11 0 0
y.SSM$Q
## , , 1
##
## [,1] [,2]
## [1,] NA 0
## [2,] 0 NA
y.SSM$Z
## , , 1
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.2733 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 2
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.27923 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 3
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.28217 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 4
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.29389 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 5
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.29244 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 6
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.29679 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 7
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.26554 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 8
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.26263 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 9
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.26554 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 10
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.27277 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 11
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.27565 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 12
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.28281 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 13
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.28992 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 14
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.29557 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 15
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.30119 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 16
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.31647 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 17
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.31923 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 18
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.32197 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 19
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.33017 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 20
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.32882 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 21
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.32867 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 22
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.33945 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 23
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.34613 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 24
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.35276 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 25
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.33577 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 26
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.34227 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 27
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.35002 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 28
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.35694 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 29
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.36321 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 30
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.36945 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 31
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.37565 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 32
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.37688 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 33
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.37812 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 34
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.38304 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 35
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.38916 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 36
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.39402 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 37
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.40007 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 38
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.40488 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 39
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.40848 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 40
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.418 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 41
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.42273 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 42
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.42861 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 43
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.42022 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 44
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.42836 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 45
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.41979 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 46
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.43353 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 47
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.43693 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 48
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.44144 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 49
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.44819 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 50
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.45489 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 51
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.46043 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 52
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.47906 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 53
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.46993 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 54
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.47531 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 55
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.47958 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 56
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.48278 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 57
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.49125 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 58
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.5111 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 59
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.49068 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 60
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.36244 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 61
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.38163 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 62
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.22413 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 63
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.23295 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 64
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.17118 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 65
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.18521 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 66
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.19538 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 67
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.20454 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 68
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.2238 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 69
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.23467 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 70
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.2543 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 71
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.12563 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 72
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.14028 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 73
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.0172 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 74
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.03374 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 75
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.05324 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 76
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.09113 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 77
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.13211 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 78
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.15126 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 79
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.16142 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 80
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.16717 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 81
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.17575 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 82
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.18988 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 83
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.20174 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 84
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.16044 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 85
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.17337 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 86
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.18614 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 87
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.19146 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 88
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.21053 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 89
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.22155 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 90
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.22669 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 91
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.21563 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 92
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.2296 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 93
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.24277 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 94
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.24149 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 95
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.25546 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 96
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.26865 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 97
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.28819 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 98
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.29857 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 99
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.31403 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 100
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.27793 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 101
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.27276 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 102
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.28103 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 103
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.30422 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 104
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.37907 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 105
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.38798 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 106
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.39993 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 107
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.40771 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 108
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.41541 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 109
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.4254 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 110
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.42642 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 111
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.44464 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 112
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.46516 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 113
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.4702 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 114
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.47181 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 115
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.47277 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 116
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.4817 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 117
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.4839 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 118
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.49199 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 119
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.46234 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 120
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.46781 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 121
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.47149 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 122
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.46097 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 123
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.43544 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 124
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.4037 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 125
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.39928 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 126
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.21877 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 127
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.17031 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 128
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.18043 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 129
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.19534 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 130
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.21525 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 131
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.22842 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 132
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.22932 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 133
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.26553 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 134
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.23386 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 135
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.23143 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 136
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.19198 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 137
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.20149 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 138
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.19055 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 139
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.20962 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 140
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.22383 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 141
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.24191 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 142
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.26151 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 143
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.28343 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 144
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.27503 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 145
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.25608 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 146
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.26334 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 147
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.14853 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 148
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.16142 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 149
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.18046 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 150
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.17278 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 151
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.12764 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 152
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.08353 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 153
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.09376 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 154
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.11463 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 155
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.11156 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 156
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.14585 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 157
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.18258 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 158
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.22489 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 159
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.21789 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 160
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.1956 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 161
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.19549 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 162
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.15888 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 163
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.16484 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 164
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.14381 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 165
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.12799 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 166
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.13736 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 167
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.14175 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 168
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.14568 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 169
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.18382 0 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 170
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.17457 1 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 171
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.17909 1 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 172
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.13288 1 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 173
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.13733 1 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 174
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.13973 1 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 175
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.11977 1 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 176
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.12496 1 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 177
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.12963 1 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 178
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.13316 1 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 179
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.13693 1 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 180
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.13956 1 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 181
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.13897 1 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 182
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.16459 1 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 183
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.15645 1 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 184
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.15973 1 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 185
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.16443 1 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 186
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.16476 1 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 187
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.16338 1 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 188
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.16459 1 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 189
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.17074 1 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 190
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.15016 1 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 191
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.15394 1 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
##
## , , 192
##
## log(PetrolPrice) law level sea_dummy1 sea_dummy2 sea_dummy3
## [1,] -2.15359 1 1 1 0 0
## sea_dummy4 sea_dummy5 sea_dummy6 sea_dummy7 sea_dummy8 sea_dummy9
## [1,] 0 0 0 0 0 0
## sea_dummy10 sea_dummy11
## [1,] 0 0
y.SSM$H
## , , 1
##
## [,1]
## [1,] NA
# define update function for maximum likelihhod estimation
updatefn_KSI <- function(pars,model,...){
model$H[] <- exp(pars[1])
diag(model$Q[,,1])<- exp(c(pars[2:3]))
model
}
# estimate model parameters using maximum likelihhod
y.ML <- fitSSM(inits=log(c(var(log(Seatbelts[,'drivers'])), 0.001, 0.0001)),
model=y.SSM,
updatefn=updatefn_KSI,
method='BFGS')
str(y.ML$model)
## List of 14
## $ y : ts [1:192, 1] 7.43 7.32 7.32 7.23 7.4 ...
## ..- attr(*, "tsp")= num [1:3] 1969 1985 12
## $ Z : num [1, 1:14, 1:192] -2.27 0 1 1 0 ...
## ..- attr(*, "dimnames")=List of 3
## .. ..$ : NULL
## .. ..$ : chr [1:14] "log(PetrolPrice)" "law" "level" "sea_dummy1" ...
## .. ..$ : NULL
## $ H : num [1, 1, 1] 0.00403
## $ T : num [1:14, 1:14, 1] 1 0 0 0 0 0 0 0 0 0 ...
## ..- attr(*, "dimnames")=List of 3
## .. ..$ : chr [1:14] "log(PetrolPrice)" "law" "level" "sea_dummy1" ...
## .. ..$ : chr [1:14] "log(PetrolPrice)" "law" "level" "sea_dummy1" ...
## .. ..$ : NULL
## $ R : num [1:14, 1:2, 1] 0 0 1 0 0 0 0 0 0 0 ...
## ..- attr(*, "dimnames")=List of 3
## .. ..$ : chr [1:14] "log(PetrolPrice)" "law" "level" "sea_dummy1" ...
## .. ..$ : NULL
## .. ..$ : NULL
## $ Q : num [1:2, 1:2, 1] 2.68e-04 0.00 0.00 1.02e-07
## $ a1 : num [1:14, 1] 0 0 0 0 0 0 0 0 0 0 ...
## ..- attr(*, "dimnames")=List of 2
## .. ..$ : chr [1:14] "log(PetrolPrice)" "law" "level" "sea_dummy1" ...
## .. ..$ : NULL
## $ P1 : num [1:14, 1:14] 0 0 0 0 0 0 0 0 0 0 ...
## ..- attr(*, "dimnames")=List of 2
## .. ..$ : chr [1:14] "log(PetrolPrice)" "law" "level" "sea_dummy1" ...
## .. ..$ : chr [1:14] "log(PetrolPrice)" "law" "level" "sea_dummy1" ...
## $ P1inf : num [1:14, 1:14] 1 0 0 0 0 0 0 0 0 0 ...
## ..- attr(*, "dimnames")=List of 2
## .. ..$ : chr [1:14] "log(PetrolPrice)" "law" "level" "sea_dummy1" ...
## .. ..$ : chr [1:14] "log(PetrolPrice)" "law" "level" "sea_dummy1" ...
## $ u : chr "Omitted"
## $ distribution: chr "gaussian"
## $ tol : num 1.49e-08
## $ call : language SSModel(formula = log(drivers) ~ SSMtrend(1, Q = list(NA)) + SSMseasonal(period = 12, sea.type = "dummy", Q = NA) + log(PetrolPrice) + law, data = Seatbelts, ...
## $ terms :Classes 'terms', 'formula' length 3 log(drivers) ~ SSMtrend(1, Q = list(NA)) + SSMseasonal(period = 12, sea.type = "dummy", Q = NA) + log(PetrolPrice) + law
## .. ..- attr(*, "variables")= language list(log(drivers), SSMtrend(1, Q = list(NA)), SSMseasonal(period = 12, sea.type = "dummy", Q = NA), log(PetrolPrice), law)
## .. ..- attr(*, "factors")= int [1:5, 1:4] 0 1 0 0 0 0 0 1 0 0 ...
## .. .. ..- attr(*, "dimnames")=List of 2
## .. .. .. ..$ : chr [1:5] "log(drivers)" "SSMtrend(1, Q = list(NA))" "SSMseasonal(period = 12, sea.type = \"dummy\", Q = NA)" "log(PetrolPrice)" ...
## .. .. .. ..$ : chr [1:4] "SSMtrend(1, Q = list(NA))" "SSMseasonal(period = 12, sea.type = \"dummy\", Q = NA)" "log(PetrolPrice)" "law"
## .. ..- attr(*, "term.labels")= chr [1:4] "SSMtrend(1, Q = list(NA))" "SSMseasonal(period = 12, sea.type = \"dummy\", Q = NA)" "log(PetrolPrice)" "law"
## .. ..- attr(*, "specials")=Dotted pair list of 6
## .. .. ..$ SSMregression: NULL
## .. .. ..$ SSMtrend : int 2
## .. .. ..$ SSMseasonal : int 3
## .. .. ..$ SSMcycle : NULL
## .. .. ..$ SSMarima : NULL
## .. .. ..$ SSMcustom : NULL
## .. ..- attr(*, "order")= int [1:4] 1 1 1 1
## .. ..- attr(*, "intercept")= int 1
## .. ..- attr(*, "response")= int 1
## .. ..- attr(*, ".Environment")=<environment: R_GlobalEnv>
## - attr(*, "class")= chr "SSModel"
## - attr(*, "p")= int 1
## - attr(*, "m")= int 14
## - attr(*, "k")= int 2
## - attr(*, "n")= int 192
## - attr(*, "tv")= int [1:5] 1 0 0 0 0
## - attr(*, "state_types")= chr [1:14] "regression" "regression" "level" "seasonal" ...
## - attr(*, "eta_types")= chr [1:2] "level" "seasonal"
# estimated parameters - variance of innovations in measurement equation, state level equation, seasonal component equation
res <- data.frame(sigma2.measurement = y.ML$model$H[,,1],
sigma2.level = diag(y.ML$model$Q[,,1])[1],
sigma2.seasonality = diag(y.ML$model$Q[,,1])[2])
res
## sigma2.measurement sigma2.level sigma2.seasonality
## 1 0.004033534 0.0002682642 1.018817e-07
y.ML$model$Q
## , , 1
##
## [,1] [,2]
## [1,] 0.0002682642 0.000000e+00
## [2,] 0.0000000000 1.018817e-07
y.ML$model$H
## , , 1
##
## [,1]
## [1,] 0.004033534
# Kalman filtering and smoothing
y.KFS <- KFS(y.ML$model, filtering=c('state'), smoothing=c('state','disturbance','mean'))
y.KFS
## Smoothed values of states and standard errors at time n = 192:
## Estimate Std. Error
## log(PetrolPrice) -0.276747 0.098423
## law -0.237590 0.046454
## level 6.870292 0.219508
## sea_dummy1 0.241196 0.015869
## sea_dummy2 0.186173 0.015846
## sea_dummy3 0.080827 0.015845
## sea_dummy4 0.004022 0.015787
## sea_dummy5 -0.031093 0.015785
## sea_dummy6 -0.039204 0.015817
## sea_dummy7 -0.088493 0.015795
## sea_dummy8 -0.052943 0.015788
## sea_dummy9 -0.141188 0.015814
## sea_dummy10 -0.064414 0.015832
## sea_dummy11 -0.103432 0.015868
# smoothed state
str(y.KFS$alphahat)
## mts [1:192, 1:14] -0.277 -0.277 -0.277 -0.277 -0.277 ...
## - attr(*, "dimnames")=List of 2
## ..$ : NULL
## ..$ : chr [1:14] "log(PetrolPrice)" "law" "level" "sea_dummy1" ...
## - attr(*, "tsp")= num [1:3] 1969 1985 12
## - attr(*, "class")= chr [1:3] "mts" "ts" "matrix"
dimnames(y.KFS$alphahat)
## [[1]]
## NULL
##
## [[2]]
## [1] "log(PetrolPrice)" "law" "level"
## [4] "sea_dummy1" "sea_dummy2" "sea_dummy3"
## [7] "sea_dummy4" "sea_dummy5" "sea_dummy6"
## [10] "sea_dummy7" "sea_dummy8" "sea_dummy9"
## [13] "sea_dummy10" "sea_dummy11"
# number of observations
T <- dim(Seatbelts)[1]
# estimated parameters for two explanatory variables
y.KFS$alphahat[T,1]
## log(PetrolPrice)
## -0.2767469
y.KFS$alphahat[T,2]
## law
## -0.2375903
# actual values
y <- log(Seatbelts[,"drivers"])
# extract smoothed level, seasonal, and irregular components
y.lvl.KS <- y.KFS$alphahat[,1]*log(as.data.frame(Seatbelts)$PetrolPrice) + y.KFS$alphahat[,2]*(as.data.frame(Seatbelts)$law) + y.KFS$alphahat[,"level"]
y.sea.KS <- y.KFS$alphahat[,"sea_dummy1"]
y.eps.KS <- y.KFS$epshat
# smoothed data combinining level, seasonal, and effects of exogenous variables
y.KS_all <- rep(NA, T)
for (t in 1:T) { y.KS_all[t] <- y.KFS$alphahat[t,] %*% y.KFS$model$Z[,,t] }
# can be also obtained using predit function with missing n.ahead option
y.KS_all.CI <- predict(y.KFS$model, interval="confidence", level=0.9)
# check to see that the above two methods yield same results
cbind(y.KS_all, y.KS_all.CI)
## y.KS_all y.KS_all.CI.fit y.KS_all.CI.lwr y.KS_all.CI.upr
## Jan 1969 7.419057 7.419057 7.364537 7.473578
## Feb 1969 7.308037 7.308037 7.257284 7.358790
## Mar 1969 7.346206 7.346206 7.297824 7.394587
## Apr 1969 7.273170 7.273170 7.226200 7.320140
## May 1969 7.364113 7.364113 7.318093 7.410132
## Jun 1969 7.330525 7.330525 7.284949 7.376101
## Jul 1969 7.372738 7.372738 7.327592 7.417885
## Aug 1969 7.382938 7.382938 7.337935 7.427941
## Sep 1969 7.420724 7.420724 7.375804 7.465644
## Oct 1969 7.505257 7.505257 7.460342 7.550173
## Nov 1969 7.623583 7.623583 7.578744 7.668421
## Dec 1969 7.689195 7.689195 7.644406 7.733983
## Jan 1970 7.468326 7.468326 7.423702 7.512951
## Feb 1970 7.367794 7.367794 7.323189 7.412399
## Mar 1970 7.410780 7.410780 7.366207 7.455353
## Apr 1970 7.338423 7.338423 7.293833 7.383014
## May 1970 7.426729 7.426729 7.382179 7.471280
## Jun 1970 7.395433 7.395433 7.350864 7.440001
## Jul 1970 7.455219 7.455219 7.410590 7.499848
## Aug 1970 7.468242 7.468242 7.423685 7.512800
## Sep 1970 7.506656 7.506656 7.462096 7.551216
## Oct 1970 7.593712 7.593712 7.549130 7.638294
## Nov 1970 7.707560 7.707560 7.662972 7.752148
## Dec 1970 7.770373 7.770373 7.725735 7.815012
## Jan 1971 7.536070 7.536070 7.491372 7.580768
## Feb 1971 7.423710 7.423710 7.379071 7.468349
## Mar 1971 7.463237 7.463237 7.418655 7.507819
## Apr 1971 7.388934 7.388934 7.344373 7.433495
## May 1971 7.479220 7.479220 7.434670 7.523769
## Jun 1971 7.444332 7.444332 7.399771 7.488892
## Jul 1971 7.493027 7.493027 7.448430 7.537624
## Aug 1971 7.499115 7.499115 7.454566 7.543664
## Sep 1971 7.527827 7.527827 7.483277 7.572378
## Oct 1971 7.608560 7.608560 7.563956 7.653165
## Nov 1971 7.719065 7.719065 7.674475 7.763655
## Dec 1971 7.779248 7.779248 7.734633 7.823863
## Jan 1972 7.557916 7.557916 7.513284 7.602549
## Feb 1972 7.451520 7.451520 7.406911 7.496130
## Mar 1972 7.493795 7.493795 7.449219 7.538371
## Apr 1972 7.420776 7.420776 7.376189 7.465363
## May 1972 7.515568 7.515568 7.471019 7.560116
## Jun 1972 7.481917 7.481917 7.437310 7.526523
## Jul 1972 7.526447 7.526447 7.481891 7.571003
## Aug 1972 7.530516 7.530516 7.485963 7.575069
## Sep 1972 7.563440 7.563440 7.518870 7.608010
## Oct 1972 7.649640 7.649640 7.605061 7.694220
## Nov 1972 7.765695 7.765695 7.721114 7.810276
## Dec 1972 7.830492 7.830492 7.785882 7.875102
## Jan 1973 7.604723 7.604723 7.560096 7.649350
## Feb 1973 7.496810 7.496810 7.452185 7.541436
## Mar 1973 7.533635 7.533635 7.489007 7.578264
## Apr 1973 7.465790 7.465790 7.420879 7.510700
## May 1973 7.548225 7.548225 7.503575 7.592874
## Jun 1973 7.507205 7.507205 7.462293 7.552118
## Jul 1973 7.551124 7.551124 7.505904 7.596344
## Aug 1973 7.549787 7.549787 7.504454 7.595119
## Sep 1973 7.576442 7.576442 7.530655 7.622230
## Oct 1973 7.643622 7.643622 7.596759 7.690484
## Nov 1973 7.728563 7.728563 7.681415 7.775712
## Dec 1973 7.737886 7.737886 7.693278 7.782494
## Jan 1974 7.504642 7.504642 7.459504 7.549781
## Feb 1974 7.351384 7.351384 7.304835 7.397934
## Mar 1974 7.397322 7.397322 7.352142 7.442502
## Apr 1974 7.311657 7.311657 7.265198 7.358116
## May 1974 7.417279 7.417279 7.371753 7.462805
## Jun 1974 7.395379 7.395379 7.350645 7.440114
## Jul 1974 7.451533 7.451533 7.407000 7.496065
## Aug 1974 7.467100 7.467100 7.422441 7.511760
## Sep 1974 7.502268 7.502268 7.457320 7.547216
## Oct 1974 7.574881 7.574881 7.529267 7.620496
## Nov 1974 7.630886 7.630886 7.585714 7.676059
## Dec 1974 7.675118 7.675118 7.630474 7.719762
## Jan 1975 7.396808 7.396808 7.347963 7.445653
## Feb 1975 7.280143 7.280143 7.232876 7.327410
## Mar 1975 7.319602 7.319602 7.273447 7.365757
## Apr 1975 7.242559 7.242559 7.197615 7.287504
## May 1975 7.332084 7.332084 7.287516 7.376653
## Jun 1975 7.292159 7.292159 7.247596 7.336722
## Jul 1975 7.336844 7.336844 7.292226 7.381461
## Aug 1975 7.343275 7.343275 7.298714 7.387836
## Sep 1975 7.377575 7.377575 7.333023 7.422127
## Oct 1975 7.452805 7.452805 7.408249 7.497362
## Nov 1975 7.562716 7.562716 7.518066 7.607367
## Dec 1975 7.608194 7.608194 7.563414 7.652973
## Jan 1976 7.375143 7.375143 7.330410 7.419876
## Feb 1976 7.268159 7.268159 7.223526 7.312792
## Mar 1976 7.300382 7.300382 7.255790 7.344974
## Apr 1976 7.224207 7.224207 7.179647 7.268768
## May 1976 7.309660 7.309660 7.265120 7.354199
## Jun 1976 7.268130 7.268130 7.223566 7.312693
## Jul 1976 7.313059 7.313059 7.268528 7.357591
## Aug 1976 7.322538 7.322538 7.278006 7.367071
## Sep 1976 7.367543 7.367543 7.323005 7.412081
## Oct 1976 7.448446 7.448446 7.403765 7.493127
## Nov 1976 7.561047 7.561047 7.516441 7.605653
## Dec 1976 7.621794 7.621794 7.577188 7.666401
## Jan 1977 7.389435 7.389435 7.344809 7.434062
## Feb 1977 7.274108 7.274108 7.229485 7.318732
## Mar 1977 7.312983 7.312983 7.268316 7.357650
## Apr 1977 7.226001 7.226001 7.181326 7.270675
## May 1977 7.311164 7.311164 7.266116 7.356211
## Jun 1977 7.281018 7.281018 7.236119 7.325918
## Jul 1977 7.336824 7.336824 7.292153 7.381495
## Aug 1977 7.366071 7.366071 7.321263 7.410879
## Sep 1977 7.401492 7.401492 7.356835 7.446149
## Oct 1977 7.484662 7.484662 7.440088 7.529237
## Nov 1977 7.598990 7.598990 7.554390 7.643589
## Dec 1977 7.662779 7.662779 7.618139 7.707418
## Jan 1978 7.436823 7.436823 7.392178 7.481468
## Feb 1978 7.319673 7.319673 7.275066 7.364280
## Mar 1978 7.360329 7.360329 7.315688 7.404970
## Apr 1978 7.286334 7.286334 7.241475 7.331193
## May 1978 7.373058 7.373058 7.328344 7.417773
## Jun 1978 7.341504 7.341504 7.296682 7.386325
## Jul 1978 7.391271 7.391271 7.346394 7.436148
## Aug 1978 7.400636 7.400636 7.355710 7.445562
## Sep 1978 7.435062 7.435062 7.390158 7.479966
## Oct 1978 7.514865 7.514865 7.469903 7.559827
## Nov 1978 7.618606 7.618606 7.573923 7.663289
## Dec 1978 7.681226 7.681226 7.636207 7.726245
## Jan 1979 7.452803 7.452803 7.407450 7.498156
## Feb 1979 7.337836 7.337836 7.292281 7.383391
## Mar 1979 7.373784 7.373784 7.328393 7.419175
## Apr 1979 7.285609 7.285609 7.240396 7.330821
## May 1979 7.369877 7.369877 7.324252 7.415502
## Jun 1979 7.282994 7.282994 7.236583 7.329405
## Jul 1979 7.318591 7.318591 7.271138 7.366043
## Aug 1979 7.332907 7.332907 7.286489 7.379325
## Sep 1979 7.374469 7.374469 7.328868 7.420069
## Oct 1979 7.457055 7.457055 7.411946 7.502164
## Nov 1979 7.569484 7.569484 7.524779 7.614189
## Dec 1979 7.625542 7.625542 7.580884 7.670200
## Jan 1980 7.398756 7.398756 7.353981 7.443532
## Feb 1980 7.272637 7.272637 7.228029 7.317246
## Mar 1980 7.309339 7.309339 7.264764 7.353913
## Apr 1980 7.219527 7.219527 7.174729 7.264324
## May 1980 7.308526 7.308526 7.263809 7.353244
## Jun 1980 7.269920 7.269920 7.225192 7.314647
## Jul 1980 7.320581 7.320581 7.276043 7.365118
## Aug 1980 7.331020 7.331020 7.286483 7.375557
## Sep 1980 7.368414 7.368414 7.323825 7.413002
## Oct 1980 7.449520 7.449520 7.404840 7.494200
## Nov 1980 7.555781 7.555781 7.510537 7.601025
## Dec 1980 7.609697 7.609697 7.564437 7.654956
## Jan 1981 7.375564 7.375564 7.330620 7.420507
## Feb 1981 7.274698 7.274698 7.229277 7.320119
## Mar 1981 7.290340 7.290340 7.245135 7.335545
## Apr 1981 7.222208 7.222208 7.177540 7.266877
## May 1981 7.319112 7.319112 7.274564 7.363660
## Jun 1981 7.284280 7.284280 7.239699 7.328860
## Jul 1981 7.327285 7.327285 7.282627 7.371942
## Aug 1981 7.324360 7.324360 7.278667 7.370054
## Sep 1981 7.363753 7.363753 7.318325 7.409181
## Oct 1981 7.443589 7.443589 7.398448 7.488730
## Nov 1981 7.536978 7.536978 7.491783 7.582173
## Dec 1981 7.590670 7.590670 7.546024 7.635316
## Jan 1982 7.366464 7.366464 7.321827 7.411102
## Feb 1982 7.270019 7.270019 7.224484 7.315554
## Mar 1982 7.310510 7.310510 7.265169 7.355850
## Apr 1982 7.232803 7.232803 7.187813 7.277792
## May 1982 7.327153 7.327153 7.282179 7.372127
## Jun 1982 7.289138 7.289138 7.244205 7.334070
## Jul 1982 7.343600 7.343600 7.298420 7.388780
## Aug 1982 7.351981 7.351981 7.306499 7.397462
## Sep 1982 7.383667 7.383667 7.337451 7.429884
## Oct 1982 7.464679 7.464679 7.417577 7.511781
## Nov 1982 7.568977 7.568977 7.520520 7.617433
## Dec 1982 7.620770 7.620770 7.570002 7.671537
## Jan 1983 7.393088 7.393088 7.338483 7.447693
## Feb 1983 7.040964 7.040964 6.986444 7.095485
## Mar 1983 7.086401 7.086401 7.035473 7.137329
## Apr 1983 7.000783 7.000783 6.952388 7.049177
## May 1983 7.090050 7.090050 7.043118 7.136982
## Jun 1983 7.052997 7.052997 7.006991 7.099003
## Jul 1983 7.099380 7.099380 7.053890 7.144870
## Aug 1983 7.113619 7.113619 7.068455 7.158783
## Sep 1983 7.159753 7.159753 7.114779 7.204727
## Oct 1983 7.240375 7.240375 7.195450 7.285300
## Nov 1983 7.345338 7.345338 7.300536 7.390139
## Dec 1983 7.402558 7.402558 7.357808 7.447307
## Jan 1984 7.176581 7.176581 7.131622 7.221540
## Feb 1984 7.076102 7.076102 7.031323 7.120882
## Mar 1984 7.118319 7.118319 7.073548 7.163090
## Apr 1984 7.045385 7.045385 7.000531 7.090239
## May 1984 7.140076 7.140076 7.095127 7.185026
## Jun 1984 7.107918 7.107918 7.062728 7.153109
## Jul 1984 7.162150 7.162150 7.116613 7.207686
## Aug 1984 7.179504 7.179504 7.133463 7.225546
## Sep 1984 7.226679 7.226679 7.179732 7.273626
## Oct 1984 7.304920 7.304920 7.256469 7.353371
## Nov 1984 7.414647 7.414647 7.363903 7.465391
## Dec 1984 7.469898 7.469898 7.415459 7.524336
par(mfrow=c(3,1), cex=0.7)
# actual data and smoothed state component
tmp <- ts( cbind(y, y.lvl.KS), start=1969, frequency=12 )
plot.ts(tmp, plot.type="single", xlab="", ylab="log KSI", col=c("darkgrey","red"), lwd=c(1,2))
abline(v=1969:2003, lty= "dotted",col="lightgrey")
legend("topright", c("actual data","Kalman smoothed level"), col=c("darkgrey","red"), lwd=c(1,2), bty="n")
# smoothed seasonal component
tmp <- ts( y.sea.KS, start=1969, frequency=12)
plot(tmp,xlab="",ylab = "log KSI", col = "red",lwd=2)
abline(h=0,col="grey")
abline(v=1969:2003, lty= "dotted",col="lightgrey")
legend("topright", "Kalman smoothed seasonal component", col="red", lwd=2, bty="n")
# smoothed irregular component
tmp <- ts( y.eps.KS, start=1969, frequency=12)
plot(tmp, xlab="", ylab="log KSI", col="red", lwd=2)
abline(h=0,col="grey")
abline(v=1969:2003, lty= "dotted",col="lightgrey")
legend("topright", "irregular component", col="red", lwd=2, bty="n")
