# Continuous Time Optimisation Help # Continuous Time Optimization Help

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One of the topics covered by our statistics homework help is continuous time optimization. Statistics students in Australia, UK, USA, Middle East, Malaysia, Singapore, etc. struggling with this topic can now rest easy. They can contact our experts at any time and receive accurate solutions.

To prove to you that our experts are knowledgeable in this area, we have discussed some of the topics under continuous time optimization below:

• Confidence intervals assignment help

Confidence interval reveals how much uncertainty a particular statistic has. It is often with a margin of error. A confidence interval tells us if the results from a survey are what we would expect if it were possible to research the whole population. 99%, 95%, and 90% are the most commonly used confidence interval.

Our experts can solve your tough questions on confidence intervals and provide you with detailed explanations. Get our continuous optimization assignment help whenever you need help with your assignment. We are at your disposal, 24×7.

• Ito’s lemma assignment help

The Ito’s lemma is used to determine a time-dependent stochastic process’ derivate. This component is intrinsic to the derivation of the Black-Scholes equation for contingent options pricing. It is also the foundation of quantitative finance.  To understand the Ito’s lemma, you must have background knowledge of stochastic differential equations, Brownian motion, and geometric Brownian motion.

In a stochastic setting, the Ito’s lemma performs the role of the chain rule.

The chain rule

The chain rule is a fundamental tool used in ordinary calculus. It is used to perform a calculation of a derivative of chained functional composition. To cope with a random variable, the ordinary calculus version of the chain rule should be correctly extended.

Our experts are well-versed with the formulas used in chain rule and the Ito’s lemma. Get in touch with them when you are faced with an Ito’s lemma assignment that you do not comprehend. If you are unsure about the knowledge and capabilities of our statistics assignment helpers, visit our samples page. There, you will find a variety of solved assignment questions related to continuous time optimization.

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• Bang-bang control and switching functions assignment help

We know that you have probably used a water heater. Most water heaters are based on temperature feedback. They try to maintain the desired temperature by switching the power off and on. These kinds of water heaters are an example of real-world application of the bang-bang control

The bang-bang control system electronically or mechanically turns something on or off when a set point has been reached. They are sometimes called hysteresis controllers, on and off controllers, or the two step-controllers.

Understand this concept better by availing of our continuous time optimization homework help.

• Time-series analysis and forecasting assignment help

The use of particular methods to analyze and extract meaningful statistics from time-series data is known as time series analysis. On the other hand, time series forecasting involves the use of a model to predict future values from the values observed previously.

Time series analysis and forecasting is extensively used for non-stationary data such as stock price, weather, retail sales, economic data, etc.

How to model time-series data

There are a variety of ways that one can model time series data and make predictions. Our statistics tutors have discussed three methods below:

1. Moving average

Moving average is considered the most naïve approach in time series modeling. It works with a simple principle which states that the mean of all past observations is the next observation. The moving average model offers a good starting point. It can be surprisingly good at identifying exciting trends in data.

1. Exponential smoothing

Exponential smoothing model follows the same logic as the moving average. However, a different decreasing weight must be assigned to each observation. This means that the more you move further from the present, the less importance is given to observations.

This model can be expressed mathematically in the following way:

Y = axt+ (1-a)yt-1 , t > 0

Types of exponential smoothing

• Double exponential smoothing

This approach is used when there is a trend in the time series data. It is the recursive use of the exponential smoothing or using the exponential smoothing twice.

The mathematical expression of double exponential smoothing is shown in the diagram below: • Triple exponential smoothing

This is an extension of a double exponential smoothing. A seasonal smoothing factor is added to cater to seasonality in the time series. The mathematical expression of triple exponential smoothing is shown below: 3. SARIMA (Seasonal Autoregressive Intergraded Moving Average) Model

SARIMA is used to model time series that shows seasonality and non-stationary properties. It is a complex model made by a combination of simpler models:

• The Autoregression Model Ar(p)

It is the regression of the time series onto itself. The assumption made here is that the previous values determine the current value with some lag. The pis the parameter that represents the maximum lag.

• Moving average model MA(q)

The parameter q is a representation of the biggest lag. After it, other lags on the autocorrelation plot are insignificant.

• Order of integration I(d)

Parameter d is the differences needed to make the time series stationary

• Seasonality

This is the final component represented by S(P,D, Q, s). This represents the season’s length.

Combining all the parameters mentioned above gives us the SARIMA (p, d, q)( P, D, Q, s) model. Please note that before using SARIMA, transformations must be applied to the time series to eliminate non-stationary behavior and seasonality.

Are the theories and formulas discussed above too much for you to wrap your head around? Do not worry. Type the words “do my continuous time optimization assignment,” and our customer support team will link you to one of our seasoned experts.

Statistics Assignment Experts has got you covered on all matters statistics. You can also get our continuous time optimization help when you are struggling with the following topics:

• Random Variables and Processes
• Hamilton-Jacobi-bellman equation
• Control under uncertainty
• Theoretical Statistics
• Singular control. Dynamical programming
• Computational Biology And Bioinformatics
• Linear time-invariant state equations
• Verification lemma
• Transversality conditions
• Measures of Dispersion- Standard deviation, Mean deviation, Variance
• Scaling of Scores and Ratings

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