Background

There are three variables, name target,candidate and others,

• The range of target is $[a, b]$.
• The range of candidate is $[c, d]$.
• The range of others is $[e, f]$.

1. $sigmoid(value, factor=100) = (\LARGE{\frac{1}{1+e^{(-value/factor)}}}-0.5)*2$
2. $W_i = \frac{1}{N}$

Basic definition related to Bounds

Definition

Part 1: How to generate Random data with Excel

Generate Normal Distribution Ramdom Values

The following pictures show how to generate 1000 normal distribution data.
Step 1

Step 2

Step 3
Please to evaluation the distribution of the data

We have know what is the AR, ARMA model. There are relationships between ARCH and AR, GARCH and ARMA. If we know the relationshps among them, it will be very helpful for understanding what we do in this practice.

The ARCH model is appropriate when the error variance in a time series follows an autoregressive (AR) model; if an autoregressive moving average (ARMA) model is assumed for the error variance, the model is a generalized autoregressive conditional heteroskedasticity (GARCH) model.

Rainfall Modelling (W6)

Part1: Getting Gamma model parameters

• The instructions

  instructions

  1. Take the file called PoorakaMonthlyFit.xls. It contains a sheet that shows the fitting procedure using Likelihood to fit a Gamma Distribution to data for the 87 years for June for Pooraka. Try matching moments to see what you get for the parameters as well.
  2. You are to repeat this for May-September. Check out both the methods and apply to the other months. Then see about in each case.

• Setting Parameters

1 Principles of statistical forecasting

• The main item refers not only to forecasting but any type of statistical modelling.
• It is that one builds the model one part (usually the majority) of the data, and then tests the results on the remainder.
• These sets are termed the Training and Testing sets.
• In standard statistical modelling, often the sets are sampled from the data at random.
• In time series forecasting, this is not possible, as the model building set has to have consecutive data, as does the testing set.
• This is further complicated with data that includes seasonality, as at least the training set has to contain multiples of the fundamental period.
• For instance, for hourly solar radiation, the training set would comprise a number of years. We also have to cater for leap years in some way. The easiest way is to delete Feb 29.

Key Points

1. Tread
2. Seasonality
3. ARMA
4. ARCH&GARCH
5. Rain model
6. Diffuse SolarRadiation
7. Synthetic Generation

Basic Definition but Important

What is time series

A series data indexed by date.

What is power spectrum

Methods

How to remove seasonality

There are two forms of ridding the original of seasonality, by either dividing by appropriate seasonal indices or by subtracting them.