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#  第9章 状態空間モデルによる時系列の解析
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#
# AR モデルによる長期予測
## Example of prediction (AR model : m=15, k=1)
#
data(BLSALLFOOD)
#
BLS120 <- BLSALLFOOD[1:120]
z1 <- arfit(BLS120, plot = FALSE)
tau2 <- z1$sigma2
arcoef <- z1$arcoef

# in case m = 15
m1 <- z1$maice.order
f <- matrix(0.0e0, m1, m1)
f[1, ] <- arcoef[1:m1]
if (m1 != 1)
  for (i in 2:m1) f[i, i-1] <- 1
g <- c(1, rep(0.0e0, m1-1))
h <- c(1, rep(0.0e0, m1-1))
q <- tau2[m1+1]
r <- 0.0e0
x0 <- rep(0.0e0, m1)
v0 <- NULL

s1 <- tsmooth(BLS120, f, g, h, q, r, x0, v0, filter.end = 120, predict.end = 156)
s1

plot(s1, BLSALLFOOD)

######################################
#
#  AR(1) による長期予測
#
BLS120 <- BLSALLFOOD[1:120]
z1 <- arfit(BLS120, plot = FALSE, lag=1)
tau2 <- z1$sigma2
arcoef <- z1$arcoef

m1 <- z1$maice.order
f <- matrix(0.0e0, m1, m1)
f[1, ] <- arcoef[1:m1]
if (m1 != 1)
  for (i in 2:m1) f[i, i-1] <- 1
g <- c(1, rep(0.0e0, m1-1))
h <- c(1, rep(0.0e0, m1-1))
q <- tau2[m1+1]
r <- 0.0e0
x0 <- rep(0.0e0, m1)
v0 <- NULL

s1 <- tsmooth(BLS120, f, g, h, q, r, x0, v0, filter.end = 120, predict.end = 156)
s1

plot(s1, BLSALLFOOD)


#
#  AR次数 5　（下記のものに置き換える）
#
z1 <- arfit(BLSALLFOOD, plot=FALSE,lag=5)


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#
# ARモデルによる欠測値の補間
#
## AR model (l=1, k=1)　　AR次数は自動決定
#
## Example of interpolation of missing values  (AR model : m=15, k=1)
z2 <- arfit(BLSALLFOOD, plot = FALSE)
tau2 <- z2$sigma2
arcoef <- z2$arcoef

# in case m2 = 15
m2 <- z2$maice.order
f <- matrix(0.0e0, m2, m2)
f[1, ] <- arcoef[1:m2]
if (m2 != 1)
  for (i in 2:m2) f[i, i-1] <- 1
g <- c(1, rep(0.0e0, m2-1))
h <- c(1, rep(0.0e0, m2-1))
q <- tau2[m2+1]
r <- 0.0e0
x0 <- rep(0.0e0, m2)
v0 <- NULL

tsmooth(BLSALLFOOD, f, g, h, q, r, x0, v0, missed = c(41, 101), np = c(30, 20))

#########################
#
#  AR次数 1　（下記のものに置き換える）
#
z2 <- arfit(BLSALLFOOD, plot=FALSE,lag=1)
#
#  AR次数 5
#
z2 <- arfit(BLSALLFOOD, plot=FALSE,lag=5)