TIME SERIES ANALYSIS IN MCA-DS

 

·        WHAT IS A TIME SERIES?

Time-series is a set of observations over time. Time series stochastic have to process this process are discrete-time continuous-time basically time series of dependency that we want to analyze and take the advantages of understanding the past of time series and we can predict the future of time series.

These five key aims in a time series following fig-1:

FIG-1: 5 KEY AIM OF TIME SERIES

 ·        STATIONERY IN TIME SERIES

o   Stationary it is mostly usable property of time series.

o   Strictly stationary is statistical properties do not change this property over the time it is different difficult to test for statistical properties.

o   Weak stationary is if the mean is constant. If the convince depends only on the time difference (lag)

o   Importance of the stationary we can only estimate the parameter of values with historical values if the series is stationary if time series is non-stationary I can take the difference until it becomes stationary for example x_t it is not a stationary but x_{t ,} x_t - 1 is stationary.

 

·        MARKOV PROPERTY IN TIME SERIES

 

In Markov property order to forecast the future of the one simply needs present and not the past and the present containing for information the past it is also similar to Christianity salvation principle.

 

·        AUTOCOVARIENCE FUNCTION

 

Initially, Autocovariance work is utilized to assess the prevailing time frames in the time series.

The Autocovariance is simply the covariance of a variable at a few other times, estimated by a delay (or lead) τ.

The Autocovariance as an element of the delay (τ and L):

Autocovariance is characterized as the covariance between the current worth (xt) with the past esteem (xt-1) and the current worth (xt) with (xt-2). Furthermore, it is meant as Υ. Here Mean won't change in case it is a fixed time series. so equation will turn into

 

                                          Autocovariance for time series data

 

·        AUTOCORRELATION FUNCTION

Autocorrelation can be characterized as a connection among's itself and different upsides of the equivalent variable (features) (for our situation relationship among's (Xt and Xt-1) (Xt and Xt-2). and so forth…) and it is signified as ρ.

Autocorrelation function (ACF) of time series is characterized as,

 

·        WHITE NOISE

 

time-series will be used white noise.

 

A time series is a white noise these variables are independent and identically distributed into a mean of zero.

it is all about the meaning of variables that have the same variance (sigma^2) and its value has a zero correlation into all other values in these time series.

 

If the variables of the time series are created or drawn from a Gaussian distribution, that series is called Gaussian white noise.

 

 

·        ARIMA

     Arima, it is mean by  ‘Auto-Regressive Integrated Moving Average’  it is mostly using a class of models that ‘explains’ a given time series based totally on its own beyond values, it is own lags for the lagged forecast mistakes or errors, so this equation may be used to forecast future values.

     Arima models provide some other approaches to time series forecasting.That is exponential smoothing or arima models are the 2 maximum broadly durable processes to time collection forecasting and offer complementary techniques to the hassle. Whilst exponential smoothing models are primarily based on an outline of the trend and seasonality in the data, the Arima series intention to explain the autocorrelations in the information.

 

     Before we introduce an ARIMA model,  we will discuss the first concept of stationarity or the technique of differencing of the time series.

     And the ARIMA model is the 3 terms this characterizes them : p, d, q

where,

p is the use to order of the AR term

 

q is the use to order of the MA term

 

d it is the no's of differences required to make a time series stationary

 

This time series is used seasonal patterns, then we have to need to add seasonal terms or it is also known as SARIMA, which is short for ‘Seasonal ARIMA’. many on that once you finish ARIMA.

 

     Autoregression (AR):

It refers to a model that indicates a changing variable that regresses on its personal lagged, or previous, values.

 

Included (I):

It represents the differencing of raw observations to permit for the time series to     become stationary

Moving Common (MA): 

Consists of the dependency among a statement and residual errors from a shifting average version applied to lagged observations

 

·        FITTING TIME SERIES TO DATA:-

In addition to becoming parametric distribution to information, it's also viable to fit parametric time-series models to ancient facts to create forecasts. In the evaluation of time-series statistics is by way of nature sequential as the price inside the next period is related to that of previous durations.

 

·        GRACE

·       Generalized

·       Autoregressive

·       Conditional

·       Heteroskedasticity: it is a collection of random variables where there are a safe population that have different variability from others we use it to measure volatility

·        MEASURING VOLATILITY

Assumes true quality volatility is constant this is historical moving average if dealing with a large sample then you can replace n -1 with n so we can assume daily returns have a mean of zero so now we have an equally weighted moving average measuring volatility but should old data get the same as new data the more that is the more smooth less responsive to new data instead we should give more weight to new data now volatility will change over the time in a stable way to more reasonable than as moving constant volatility weighted moving average the alpha's are weights and need to some to 1. 

 I have lots of different methods of what we can help serve many of the features and there is a simple approach we can do is we can assure you that we decline exponentially since it was saying is a p-type the ratio of the two ways we wanna get Lambda and now you can modify the formula as polished and physical effort you should consider doing series of these white we just need to know what is the ratio between them sooner we made this next certification ok so we can we write the formula and change the parents can be used to go caused due to the so we have the parents of the volatility of the future is equal length one month plan the x squared circle it is the winner of focusing on the polity aspect on that if you wish to take me expected values for x squared to see that is Sigma squared and what we can do is key to open shook Ones I am we can see that all the to keep doing this we can get a flat for cost of volatility.

 

 

·        CONCLUSION

We have to learn in this Blog Time Series, the Stationary and Marker Property Auto Variance and Autocorrelation Function White Noise, ARIMA, Fitting Time Series to Data,, Grace, Measuring Volatility.

 

·        REFERENCES

https://www.udemy.com/course/time-series-for-actuaries/