Sydney weather Forcasting

-Multivariate Time Series Analysis

Chang Shen

 

CONTENTS

  • Introduction

  • Exploratory Data Analysis

  • VAR Model

  • LSTM Model

  • Forecasting Result

  • Discussion

Introduction

Weather forecasting

 

Relates closely to Production activities, social activities and

daily activities. 

 

temperature

humidity

rainfall

wind

speed

meteorology

understanding

Introduction

Multivariate Time Series Problem

A Multivariate Time Series is n time series within the same time frame

Exploratory Data Analysis

Australia weather Data 

  • Choose recordings from Sydney weather station​

 

  • 9 variables 1578 observations from 2013-03-01 to 2017-06-25

 

  • Daily Max Temperature, Min Temperature, Wind speed at 9 am and 3 pm, Humidity at 9 am and 3 pm, pressure at 9 am and 3 pm

Exploratory Data Analysis

Exploratory Data Analysis

 

After missing data imputataion

Exploratory Data Analysis

Stationary

Seasonality

ADF test

VAR(Vector Auto regression)

A generalization of AR model, VAR(p)

Y_{t}=c+A_{1} Y_{t-1}+A_{2} Y_{t-2}+\cdots+A_{p} Y_{t-p}+\epsilon_{t}

where the \(y_{t-p}\) denotes \(i th\) lag of \(y\), \(y_{t}\) is the vector \(\{y_{1,t},\cdots,y_{k,t}\},\epsilon\) is a zero-mean error term has a variance \(\sigma^2\) and \(cov(\epsilon_i,\epsilon_j)=0, \forall i \neq j\),\(A_i\) is a time-invariant \(k\times k\)-matrix

VAR(Vector Auto regression)

A generalization of AR model

VAR(Vector Auto regression)

 Determine the order p 

  • AIC and FPE tend to choose the model VAR(2)
  • HQ and SC tend to choose model VAR(1)

VAR(Vector Auto regression)

Fitting VAR model

 

  •  Split training set
  • Differenceing non stationary variable(Min Temperature)
  •  Dummy Seasonal

VAR(Vector Auto regression)

Diagnose

Portmanteau-test

 

 

ARCH Lagrange-Multiplier test

 

Normality test

LSTM(Long Short Term Memory)

Long Short Term Memory (LSTM) networks are special kind of Recurrent Neural Network (RNN) that are capable of learning long-term dependencies

LSTM(Long Short Term Memory)

Long Short Term Memory (LSTM) networks are special kind of Recurrent Neural Network (RNN) that are capable of learning long-term dependencies

LSTM(Long Short Term Memory)

1. Split training set and testing set

2. Normalize the data

3. Define model

  • Batch size
  • Time step 
  • Features

4.complie and fitting the model

Forecasting Result

Forecasting Result

Reflection

VAR

  • VAR is a powerful algorithm but it has limitation since it only applicable to numeric variables.

  • Have to choose order

  • Require the stationary presumption (may need transformation)

  • easy to understand and train

LSTM

  • A black box model can’t be written as VAR
  • Parameter tuning/ take long training time and more CPU memory
  • More suitable for large scale data
  • Can be applied to multiple scenarios like forecasting, classification, anomalously detection
  • long training time

 

THANKS