---
title: "SUTSE models"
author: "Jean Palate"
date: "`r Sys.Date()`"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{SUTSE model}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

### Introduction 

Simple SUTSE models can be easily tackled by the state space framework provided in rjd3sts


```{r echo=FALSE}

suppressPackageStartupMessages(library(rjd3toolkit))
suppressPackageStartupMessages(library(rjd3sts))
library(knitr)
```

The *sutse* function computes simple SUTSE models for wo series

```{r sutse}
sutse<-function(st){
    if (! inherits(st, "ts") || ! inherits(st, "matrix"))
        stop(st, " is not a ts matrix")
    if (dim(st)[2]!= 2)
        stop(st, " must have two columns")
    s<-st[,1]
    t<-st[,2]
    freq<-frequency(st)
    start<-start(st)
    # re-scaling of the series to minimize numerical problems
    vs<-as.numeric(var(s))
    vt<-as.numeric(var(t))
    es<-sqrt(vs)
    et<-sqrt(vt)
    s<-s/es
    t<-t/et

    model<-model()
    # create the components and add them to the model
    l1<-locallevel("l1", initial = 0)
    lt1<-locallineartrend("lt1", levelVariance = 0, fixedLevelVariance = TRUE)
    s1<-seasonal("s1", freq, type="HarrisonStevens")
    n1<-noise("n1")
    l2<-locallevel("l2", initial = 0)
    lt2<-locallineartrend("lt2", levelVariance = 0, fixedLevelVariance = TRUE)
    s2<-seasonal("s2", freq, type="HarrisonStevens")
    n2<-noise("n2")
    add(model, l1)
    add(model, lt1)
    add(model, s1)
    add(model, n1)
    add(model, l2)
    add(model, lt2)
    add(model, s2)
    add(model, n2)

    # create the equation (fix the variance to 0)
    eq1<-equation("eq1")
    add_equation(eq1, l1)
    add_equation(eq1, lt1)
    add_equation(eq1, s1)
    add_equation(eq1, n1)
    add(model, eq1)
    eq2<-equation("eq2")
    add_equation(eq2, l2)
    add_equation(eq2, l1, 0, FALSE)
    add_equation(eq2, lt2)
    add_equation(eq2, lt1, 0, FALSE)
    add_equation(eq2, s2)
    add_equation(eq2, s1, 0, FALSE)
    add_equation(eq2, n2)
    add_equation(eq2, n1, 0, FALSE)
    add(model, eq2)
    rslt<-estimate(model, cbind(s,t), marginal=TRUE, initialization="Augmented_Robust")

    p<-result(rslt, "parameters")
    factor<-result(rslt, "scalingfactor")
    cl<-p[11]
    csl<-p[12]
    cs<-p[13]
    cn<-p[14]
    names<-c("level", "slope", "seasonal", "noise")
    variable1<-data.frame(variance=c(factor*p[1]*vs,factor*p[3]*vs, factor*p[4]*vs, factor*p[5]*vs),
                          row.names = names)
    variable2<-data.frame(variance=c(factor*vt*(p[1]*cl*cl+p[6]),
                                     factor*vt*(p[3]*csl*csl+p[8]),
                                     factor*vt*(p[4]*cs*cs+p[9]),
                                     factor*vt*(p[5]*cn*cn+p[10])),
                          row.names = names)

    if (p[1]==0){
        lc<-0
    }else if (p[6] == 0){
        lc<-1
    }else{
        lc<-sign(cl)/(sqrt(1+p[6]/(cl*cl*p[1])))
    }
    if (p[3]==0){
        sc<-0
    }else if (p[8] == 0){
        sc<-1
    }else{
        sc<-sign(csl)/(sqrt(1+p[8]/(csl*csl*p[3])))
    }
    if (p[4]==0){
        ssc<-0
    }else if (p[9] == 0){
        ssc<-1
    }else{
        ssc<-sign(cs)/(sqrt(1+p[9]/(cs*cs*p[4])))
    }
    if (p[5]==0){
        nc<-0
    }else if (p[10] == 0){
        nc<-1
    }else{
        nc<-sign(cn)/(sqrt(1+p[10]/(cn*cn*p[5])))
    }
    correlations<-data.frame(variance=c(lc, sc, ssc, nc),
                             row.names = names)

    models<-list(
        variable1=variable1,
        variable2=variable2,
        correlations=correlations
    )

    ll<-result(rslt, "likelihood.ll")
    ser<-result(rslt, "likelihood.ser")
    res<-result(rslt, "likelihood.residuals")

    likelihood<-list(loglikelihood=ll, ser=ser, residuals=res)

    sm<-smoothed_states(rslt)
    decomposition1<-list(
        series=es*s,
        level=es*ts(sm[,1]+sm[,2], frequency = freq, start = start),
        seas=es*ts(sm[,4], frequency = freq, start = start),
        noise=es*ts(sm[,15], frequency = freq, start = start)
    )
    decomposition2<-list(
        series=et*t,
        level=et*ts(sm[,1]*cl+sm[,2]*csl+sm[,16]+sm[,17], frequency = freq, start = start),
        seas=et*ts(sm[,4]*cs+sm[,19], frequency = freq, start = start),
        noise=et*ts(sm[,15]*cn+sm[,30], frequency = freq, start = start)
    )
    e<-list(decomposition1=decomposition1,
            decomposition2=decomposition2)

    return (structure(
        list(model=models,
             estimation=e,
             likelihood=likelihood,
             internal=rslt)
        , class="JD3_SUTSE"))
}

plot.JD3_SUTSE<-function(q){
    if (! inherits(q, "JD3_SUTSE"))
        stop(sutse, " should be of class JD3_SUTSE")
    par(mfrow=c(2,2))
    d<-q$estimation$decomposition1
    ts.plot(ts.union(d$series, d$series-d$seas, d$level), col=c("gray", "blue", "red"))
    ts.plot(ts.union(d$seas, d$noise), col=c("magenta", "green"))
    d<-q$estimation$decomposition2
    ts.plot(ts.union(d$series, d$series-d$seas, d$level), col=c("gray", "blue", "red"))
    ts.plot(ts.union(d$seas, d$noise), col=c("magenta", "green"))

    par(mfrow=c(1,1))
}

logLik.JD3_SUTSE<-function(q){
    if (! inherits(q, "JD3_SUTSE"))
        stop(q, " should be of class JD3_SUTSE")
    return (q$likelihood$loglikelihood)
}

print.JD3_SUTSE<-function(q){
    if (! inherits(q, "JD3_SUTSE"))
        stop(q, " should be of class JD3_SUTSE")
    cat("SUTSE model\n\n")
    cat("Max likelihood = ", q$likelihood$loglikelihood, "\n\n")
    cat("Variances of series 1\n\n")
    print(q$model$variable1)
    cat("\n\nVariances of series 2\n\n")
    print(q$model$variable2)
    cat("\n\nCorrelations between innovations of the two series\n")
    print(q$model$correlations)
}

```

```{r sutse_example, fig.width=7, fig.height=5}

q<-sutse(ts.union(log(retail$RetailSalesTotal), log(retail$BookStores)))
print(q)
plot(q)
```