The document discusses time series decomposition, which involves separating a time series into different components: trend, seasonal, and irregular.
The trend component represents long-term increases or decreases in the data. The seasonal component captures regular fluctuations that occur with a fixed periodicity, such as monthly or yearly patterns. The irregular component represents stationary random fluctuations.
Time series can be decomposed additively, by adding the trend, seasonal, and irregular components, or multiplicatively, by multiplying them. The appropriate method depends on whether seasonal fluctuations vary with the overall level of the series. Decomposition aims to produce stationary irregular components that can be modeled.
1) To understand the underlying structure of Time Series represented by sequence of observations by breaking it down to its components.
2) To fit a mathematical model and proceed to forecast the future.
1) To understand the underlying structure of Time Series represented by sequence of observations by breaking it down to its components.
2) To fit a mathematical model and proceed to forecast the future.
Time Series Analysis - 1 | Time Series in R | Time Series Forecasting | Data ...Simplilearn
This Time Series Analysis (Part-1) in R presentation will help you understand what is time series, why time series, components of time series, when not to use time series, why does a time series have to be stationary, how to make a time series stationary and at the end, you will also see a use case where we will forecast car sales for 5th year using the given data. A time series is a sequence of data being recorded at specific time intervals. The past values are analyzed to forecast a future which is time-dependent. Compared to other forecast algorithms, with time series we deal with a single variable which is dependent on time. So, lets deep dive into this presentation and understand what is time series and how to implement time series using R.
Below topics are explained in this "Time Series in R Tutorial" -
1. Why time series?
2. What is time series?
3. Components of a time series
4. When not to use time series?
5. Why does a time series have to be stationary?
6. How to make a time series stationary?
7. Example: Forcast car sales for the 5th year
Become an expert in data analytics using the R programming language in this data science certification training course. You’ll master data exploration, data visualization, predictive analytics and descriptive analytics techniques with the R language. With this data science course, you’ll get hands-on practice on R CloudLab by implementing various real-life, industry-based projects in the domains of healthcare, retail, insurance, finance, airlines, music industry, and unemployment.
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1. This course forms an ideal package for aspiring data analysts aspiring to build a successful career in analytics/data science. By the end of this training, participants will acquire a 360-degree overview of business analytics and R by mastering concepts like data exploration, data visualization, predictive analytics, etc
2. According to marketsandmarkets.com, the advanced analytics market will be worth $29.53 Billion by 2019
3. Wired.com points to a report by Glassdoor that the average salary of a data scientist is $118,709
4. Randstad reports that pay hikes in the analytics industry are 50% higher than IT
The Data Science with R is recommended for:
1. IT professionals looking for a career switch into data science and analytics
2. Software developers looking for a career switch into data science and analytics
3. Professionals working in data and business analytics
4. Graduates looking to build a career in analytics and data science
5. Anyone with a genuine interest in the data science field
6. Experienced professionals who would like to harness data science in their fields
Learn more at: https://www.simplilearn.com/
Innovations in technology has revolutionized financial services to an extent that large financial institutions like Goldman Sachs are claiming to be technology companies! It is no secret that technological innovations like Data science and AI are changing fundamentally how financial products are created, tested and delivered. While it is exciting to learn about technologies themselves, there is very little guidance available to companies and financial professionals should retool and gear themselves towards the upcoming revolution.
In this master class, we will discuss key innovations in Data Science and AI and connect applications of these novel fields in forecasting and optimization. Through case studies and examples, we will demonstrate why now is the time you should invest to learn about the topics that will reshape the financial services industry of the future!
Topics in Econometrics
Data Science - Part X - Time Series ForecastingDerek Kane
This lecture provides an overview of Time Series forecasting techniques and the process of creating effective forecasts. We will go through some of the popular statistical methods including time series decomposition, exponential smoothing, Holt-Winters, ARIMA, and GLM Models. These topics will be discussed in detail and we will go through the calibration and diagnostics effective time series models on a number of diverse datasets.
Time Series Analysis - 1 | Time Series in R | Time Series Forecasting | Data ...Simplilearn
This Time Series Analysis (Part-1) in R presentation will help you understand what is time series, why time series, components of time series, when not to use time series, why does a time series have to be stationary, how to make a time series stationary and at the end, you will also see a use case where we will forecast car sales for 5th year using the given data. A time series is a sequence of data being recorded at specific time intervals. The past values are analyzed to forecast a future which is time-dependent. Compared to other forecast algorithms, with time series we deal with a single variable which is dependent on time. So, lets deep dive into this presentation and understand what is time series and how to implement time series using R.
Below topics are explained in this "Time Series in R Tutorial" -
1. Why time series?
2. What is time series?
3. Components of a time series
4. When not to use time series?
5. Why does a time series have to be stationary?
6. How to make a time series stationary?
7. Example: Forcast car sales for the 5th year
Become an expert in data analytics using the R programming language in this data science certification training course. You’ll master data exploration, data visualization, predictive analytics and descriptive analytics techniques with the R language. With this data science course, you’ll get hands-on practice on R CloudLab by implementing various real-life, industry-based projects in the domains of healthcare, retail, insurance, finance, airlines, music industry, and unemployment.
Why learn Data Science with R?
1. This course forms an ideal package for aspiring data analysts aspiring to build a successful career in analytics/data science. By the end of this training, participants will acquire a 360-degree overview of business analytics and R by mastering concepts like data exploration, data visualization, predictive analytics, etc
2. According to marketsandmarkets.com, the advanced analytics market will be worth $29.53 Billion by 2019
3. Wired.com points to a report by Glassdoor that the average salary of a data scientist is $118,709
4. Randstad reports that pay hikes in the analytics industry are 50% higher than IT
The Data Science with R is recommended for:
1. IT professionals looking for a career switch into data science and analytics
2. Software developers looking for a career switch into data science and analytics
3. Professionals working in data and business analytics
4. Graduates looking to build a career in analytics and data science
5. Anyone with a genuine interest in the data science field
6. Experienced professionals who would like to harness data science in their fields
Learn more at: https://www.simplilearn.com/
Innovations in technology has revolutionized financial services to an extent that large financial institutions like Goldman Sachs are claiming to be technology companies! It is no secret that technological innovations like Data science and AI are changing fundamentally how financial products are created, tested and delivered. While it is exciting to learn about technologies themselves, there is very little guidance available to companies and financial professionals should retool and gear themselves towards the upcoming revolution.
In this master class, we will discuss key innovations in Data Science and AI and connect applications of these novel fields in forecasting and optimization. Through case studies and examples, we will demonstrate why now is the time you should invest to learn about the topics that will reshape the financial services industry of the future!
Topics in Econometrics
Data Science - Part X - Time Series ForecastingDerek Kane
This lecture provides an overview of Time Series forecasting techniques and the process of creating effective forecasts. We will go through some of the popular statistical methods including time series decomposition, exponential smoothing, Holt-Winters, ARIMA, and GLM Models. These topics will be discussed in detail and we will go through the calibration and diagnostics effective time series models on a number of diverse datasets.
Time series analysis aids in decomposing a series into parts which.docxjuliennehar
Time series analysis aids in decomposing a series into parts which can be related to various variations. Time series decomposition was first used by astronomers to calculate planetary orbits. The assumptions for decomposition: A long-term tendency or trend, cyclic movements, a seasonal movement in each year, and residual variations. These variations have been seen as mutually independent from each other thus, indicated by an additive decomposition model. If they depend on each other then, it creates a multiplicative model. In the case, the components are the trend, seasonality, and irregular. The additive model can be used to better understand data observed such as about airline passengers per month for the last ten years. To begin, the trend part of the airline passenger time series is extracted. The computation can be done using moving average. The trend for instance, may move upwards. Next, the time series can be DeTrend by subtracting the trend from time series. Detrended data reinforces seasonal variations of time series (Dagum, 2013). Assume that magnitude is constant. The data points are averaged for each month to find out seasonality. Residual component is what remains after subtracting the trend and season from the time series. Decomposition technique is justified in this example of airline passengers. The time series is composed of a summation of the seasonal variation, trend, and residual, exhibiting additive model. A benefit of decomposition is that it offers a pictorial representation of the data which enhances making a concrete conclusion about the study. It can be used to analyze and comprehend historic time series as well as make forecasts.
Additive model is used when seasonal variation is constant over time. The seasonal variation must have the same magnitude across time to implement additive. On the other hand, multiplicative model is important when seasonal variation rises over time.
The additive model is useful when the seasonal variation is relatively constant over time. The multiplicative model is useful when the seasonal variation increases over time.
The additive decomposition is the most appropriate if the magnitude of the seasonal fluctuations, or the variation around the trend-cycle, does not vary with the level of the time series. When the variation in the seasonal pattern, or the variation around the trend-cycle, appears to be proportional to the level of the time series, then a multiplicative decomposition is more appropriate. Multiplicative decompositions are common with economic time series.
The Figure above shows an additive decomposition of these data. Three components are shown separately in the bottom three panels of. These components can be added together to reconstruct the data shown in the top panel.
Seasonal component changes slowly over time, so that any two consecutive years have similar patterns, but years far apart may have different seasonal patterns. The remainder component shown in the botto ...
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2. Time series with deterministic
components
Up until now we assumed our time series is generated by a stationary process - either a
white noise, an autoregressive, a moving-average or an ARMA process.
However, this is not usually the case with real-world data - they are often governed by a
(deterministic) trend and they might have (deterministic) cyclical or seasonal components
in addition to the irregular/remainder (stationary process) component:
Trend component - a long-term increase or decrease in the data which might not be linear.
Sometimes the trend might change direction as time increases.
Cyclical component - exists when data exhibit rises and falls that are not of fixed period. The
average length of cycles is longer than the length of a seasonal pattern. In practice, the
trend component is assumed to include also the cyclical component. Sometimes the trend
and cyclical components together are called as trend-cycle.
Seasonal component - exists when a series exhibits regular fluctuations based on the season
(e.g. every month/quarter/year). Seasonality is always of a fixed and known period.
Irregular component - a stationary process.
3. In order to remove the deterministic components, we
can decompose our time series into separate stationary
and deterministic components.
4. Time series decomposition
The general mathematical representation of the decomposition approach:
Yt = f (Tt , St , Et )
where
) Yt is the time series value (actual data) at period t;
) Tt is a deterministic trend-cycle or general movement component;
) St is a deterministic seasonal component
) Et is the irregular (remainder or residual) (stationary) component.
The exact functional form of f (·) depends on the decomposition method used.
5. Trend Stationary Time Series
A common approach is to assume that the equation has an additive
form:
Yt = Tt + St + Et
Trend, seasonal and irregular components are simply added together to give the
observed series.
Alternatively, the multiplicative decomposition has the form:
Yt = Tt · St · Et
Trend, seasonal and irregular components are multiplied together to give the
observed series.
6. Additive or multiplicative?
An additive model is appropriate if the magnitude of the seasonal
fluctuations does not vary with the level of time series;
The multiplicative model is appropriate if the seasonal fluctuations increase
or decrease proportionally with increases and decreases in the level of the
series.
Multiplicative decomposition is more prevalent with economic series because
most seasonal economic series do have seasonal variations which increase
with the level of the series.
Rather than choosing either an additive or multiplicative decomposition, we
could transform the data beforehand.
7. Transforming data of a multiplicative
model
Very often the transformed series can be modeled additively when the
original data is not additive. In particular, logarithms turn a multiplicative
relationship into an additive relationship:
) if our model is
Yt = Tt · St · Et
) then taking the logarithms of both sides gives us:
log (Yt ) = log(Tt ) + log(St ) + log(Et )
So, we can fit a multiplicative relationship by fitting a more convenient
additive relationship to the logarithms of the data and then to move back to
the original series by exponentiating.
8. Basic Steps in Decomposition
Estimate the trend. Two approaches:
) Using a smoothing procedure;
) Specifying a regression equation for the trend;
De-trending the series:
) For an additive decomposition, this is done by subtracting the trend estimates
from the series;
) For a multiplicative decomposition, this is done by dividing the series by the
estimated trend values.
Estimating the seasonal factors from the de-trended series:
) Calculate the mean (or median) values of the de-trended series for each
specific period (for example, for monthly data - to estimate the seasonal effect
of January - average the de-trended values for all January values in the series
etc);
) Alternatively, the seasonal effects could also be estimated along with the trend
by specifying a regression equation.
The number of seasonal factors is equal to the frequency of the series (e.g.
monthly data = 12 seasonal factors, quarterly data = 4, etc.).
9. Basic Steps in Decomposition
The seasonal effects should be normalized:
) For an additive model, seasonal effects are adjusted so that the average of d
seasonal components is 0 (this is equivalent to their sum being equal to 0);
) For a multiplicative model, the d seasonal effects are adjusted so that they
average to 1 (this is equivalent to their sum being equal to d );
Calculate the irregular component
Analyze the residual component. Whichever method was used to decompose
the series, the aim is to produce stationary residuals.
Choose a model to fit the stationary residuals (e.g. see ARMA models).
Forecasting can be achieved by forecasting the residuals and combining with
the forecasts of the trend and seasonal components.
10. Estimating the trend, Tt
There are various ways to estimate the trend Tt at time t but a relatively
simple procedure which does not assume any specific form of Tt is to
calculate a moving average centered on t.
A moving average is an average of a specific number of time series values
around each value of t in the time series, with the exception of the first few
and last few terms (this procedure is available in R with the decompose
function). This method smoothes the time series.
The estimation depends on the seasonality of the time series:
) If the time series has no seasonal component;
) If the time series contains a seasonal component;
Smoothing is usually done to help us better see patterns (like the trend) in
the time series by smoothing out the irregular roughness to see a clearer
signal. For seasonal data, we might smooth out the seasonality so that we
can identify the trend.
11. Estimating Tt if the time series has no
seasonal component
In order to estimate the trend, we can take any odd number, for example, if l
= 3, we can estimate an additive model:
In this case, we are calculating the averages, either:
) centered around t - one element to the left (past) and one element to the
right (future),
) or alternatively - two elements to the left of t (past values at t − 1 and t − 2).
12. Estimating Tt if the time series contains a
seasonal component
If the time series contains a seasonal component and we want to average it
out, the length of the moving average must be equal to the seasonal
frequency (for monthly series, we would take l = 12). However, there is a
slight hurdle.
Suppose, our time series begins in January (t = 1) and we average up to
December (t = 12). This averages corresponds to a time t = 6.5 (time
between June and July).
When we come to estimate seasonal effects, we need a moving average at
integer times. This can be achieved by averaging the average of January to
December and the average of February (t = 2) up to January
(t = 13). This average of the two moving averages corresponds to t = 7 and
the process is called centering.