Introduction to Time Series

class: center, middle, inverse, title-slide

.title[
# Introduction to Time Series
]
.author[
### Zhentao Shi
]
.date[
### Aug 25, 2021
]

---

## Observations over time

- Natural ordering of observations

- A single realization in history

- Macroeconomic applications
  - [FRED database](https://research.stlouisfed.org/econ/mccracken/fred-databases/)

- Financial applications
  - [Yahoo Finance](https://finance.yahoo.com/)

---

## US GDP

```r
USA= Quandl::Quandl("UNAE/GDPCD_USA")
TT = dim(USA)[1]
USA = USA[ rev(1:TT), ]
plot( x = USA$Date, y = USA[ , 10], xlab = "year", ylab = "GDP")
```

---

## USA Industrial Production

* Another example: [Quarterly US Industrial Production Index](https://fred.stlouisfed.org/series/IPB50001SQ)

--
.pull-left[

```r
quantmod::getSymbols.FRED(
  Symbols = "IPB50001SQ", 
  env = .GlobalEnv) 
```

```
## [1] "IPB50001SQ"
```
]
.pull-right[

```r
plot(IPB50001SQ)
```

![](ts_slides1_files/figure-html/unnamed-chunk-1-1.png)
]

---

## S&P 500 Index

```r
SPX <- quantmod::getSymbols("^GSPC",
                            auto.assign = FALSE, 
                            from = "2000-01-01")$GSPC.Close
plot(SPX)
```

<img src="ts_slides1_files/figure-html/unnamed-chunk-2-1.png" width="50%" />
---

## S&P 500 Return

```r
plot( diff( log(SPX) ) )
```

---

## Bitcoin

```r
BTC <- quantmod::getSymbols("BTC-USD", auto.assign = FALSE, 
                            from = "2021-07-01")[,4]
plot(BTC)

ETH <- quantmod::getSymbols("ETH-USD", auto.assign = FALSE, 
                            from = "2021-07-01")[,4]
plot(ETH)
```

---

```r
plot( x = as.vector(ETH), y = as.vector(BTC), type = "l")
```

![](ts_slides1_files/figure-html/unnamed-chunk-5-1.png)

---

## Bitcoin return

```r
plot( diff( log(BTC) ) )
```

---

## Exchange rates

```r
quantmod::getFX("USD/JPY")
```

```
## [1] "USD/JPY"
```

```r
quantmod::getFX("HKD/JPY")
```

```
## [1] "HKD/JPY"
```

---

```r
matplot( y = cbind(USDJPY, HKDJPY*7.8), 
         x = index(USDJPY), type = "l", xlab = "time"  )
```

![](ts_slides1_files/figure-html/unnamed-chunk-8-1.png)

---

## Understanding time series

* Structural versus non-structural
* Model time series
* Extrapolate time series
  * Nowcast
  * Forecast