· 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 xt it is not
a stationary but xt , xt - 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/
