index.Rmd

---
title       : Forecasting
subtitle    : 
author      : Jeffrey Leek, Assistant Professor of Biostatistics 
job         : Johns Hopkins Bloomberg School of Public Health
logo        : bloomberg_shield.png
framework   : io2012        # {io2012, html5slides, shower, dzslides, ...}
highlighter : highlight.js  # {highlight.js, prettify, highlight}
hitheme     : tomorrow   # 
url:
  lib: ../../libraries
  assets: ../../assets
widgets     : [mathjax]            # {mathjax, quiz, bootstrap}
mode        : selfcontained # {standalone, draft}
---


```{r setup, cache = F, echo = F, message = F, warning = F, tidy = F}
# make this an external chunk that can be included in any file
options(width = 100)
opts_chunk$set(message = F, error = F, warning = F, comment = NA, fig.align = 'center', dpi = 100, tidy = F, cache.path = '.cache/', fig.path = 'fig/',cache=TRUE)

options(xtable.type = 'html')
knit_hooks$set(inline = function(x) {
  if(is.numeric(x)) {
    round(x, getOption('digits'))
  } else {
    paste(as.character(x), collapse = ', ')
  }
})
knit_hooks$set(plot = knitr:::hook_plot_html)
```

## Time series data

<img class=center src=../../assets/img/08_PredictionAndMachineLearning/GOOG.png height=450>

[https://www.google.com/finance](https://www.google.com/finance)

---

## What is different?

* Data are dependent over time
* Specific pattern types
  * Trends - long term increase or decrease
  * Seasonal patterns - patterns related to time of week, month, year, etc.
  * Cycles - patterns that rise and fall periodically
* Subsampling into training/test is more complicated
* Similar issues arise in spatial data 
  * Dependency between nearby observations
  * Location specific effects
* Typically goal is to predict one or more observations into the future. 
* All standard predictions can be used (with caution!)

---

## Beware spurious correlations!


<img class=center src=../../assets/img/08_PredictionAndMachineLearning/spurious.jpg height=450>

[http://www.google.com/trends/correlate](http://www.google.com/trends/correlate)

[http://www.newscientist.com/blogs/onepercent/2011/05/google-correlate-passes-our-we.html](http://www.newscientist.com/blogs/onepercent/2011/05/google-correlate-passes-our-we.html)

---

## Also common in geographic analyses

<img class=center src=../../assets/img/08_PredictionAndMachineLearning/heatmap.png height=450>

[http://xkcd.com/1138/](http://xkcd.com/1138/)


---

## Beware extrapolation!

<img class=center src=../../assets/img/08_PredictionAndMachineLearning/extrapolation.jpg height=450>

[http://www.nature.com/nature/journal/v431/n7008/full/431525a.html](http://www.nature.com/nature/journal/v431/n7008/full/431525a.html)

---

## Google data


```{r loadGOOG}
library(quantmod)
library(forecast)
from.dat <- as.Date("01/01/08", format="%m/%d/%y")
to.dat <- as.Date("12/31/13", format="%m/%d/%y")
getSymbols("GOOG", src="google", from = from.dat, to = to.dat)
head(GOOG)
```

---

## Summarize monthly and store as time series

```{r tseries,dependson="loadGOOG",fig.height=4,fig.width=4}
mGoog <- to.monthly(GOOG)
googOpen <- Op(mGoog)
ts1 <- ts(googOpen,frequency=12)
plot(ts1,xlab="Years+1", ylab="GOOG")
```


---

## Example time series decomposition

* __Trend__  - Consistently increasing pattern over time 
* __Seasonal__ -  When there is a pattern over a fixed period of time that recurs.
* __Cyclic__ -  When data rises and falls over non fixed periods

[https://www.otexts.org/fpp/6/1](https://www.otexts.org/fpp/6/1)


---

## Decompose a time series into parts

```{r ,dependson="tseries",fig.height=4.5,fig.width=4.5}
plot(decompose(ts1),xlab="Years+1")
```

---

## Training and test sets

```{r trainingTest,dependson="tseries",fig.height=4.5,fig.width=4.5}
ts1Train <- window(ts1,start=1,end=5)
ts1Test <- window(ts1,start=5,end=(7-0.01))
ts1Train
```

---

## Simple moving average

$$ Y_{t}=\frac{1}{2*k+1}\sum_{j=-k}^k {y_{t+j}}$$

```{r ,dependson="trainingTest",fig.height=4.5,fig.width=4.5}
plot(ts1Train)
lines(ma(ts1Train,order=3),col="red")
```



---

## Exponential smoothing

__Example - simple exponential smoothing__
$$\hat{y}_{t+1} = \alpha y_t + (1-\alpha)\hat{y}_{t-1}$$

<img class=center src=../../assets/img/08_PredictionAndMachineLearning/expsmooth.png height=300>

[https://www.otexts.org/fpp/7/6](https://www.otexts.org/fpp/7/6)

---

## Exponential smoothing

```{r ets,dependson="trainingTest",fig.height=4.5,fig.width=4.5}
ets1 <- ets(ts1Train,model="MMM")
fcast <- forecast(ets1)
plot(fcast); lines(ts1Test,col="red")
```


---

## Get the accuracy

```{r ,dependson="ets",fig.height=4.5,fig.width=4.5}
accuracy(fcast,ts1Test)
```

---

## Notes and further resources

* [Forecasting and timeseries prediction](http://en.wikipedia.org/wiki/Forecasting) is an entire field
* Rob Hyndman's [Forecasting: principles and practice](https://www.otexts.org/fpp/) is a good place to start
* Cautions
  * Be wary of spurious correlations
  * Be careful how far you predict (extrapolation)
  * Be wary of dependencies over time
* See [quantmod](http://cran.r-project.org/web/packages/quantmod/quantmod.pdf) or [quandl](http://www.quandl.com/help/packages/r) packages for finance-related problems.