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Time Series Analysis
A time series is a sequence of points of data that are ordered in a period. Time in this type of analysis is usually independent. The main aim of time series is to predict what the future holds. Some of the aspects involved in time series include seasonality, stationary, and autocorrelated. There are a plethora of ways of making predictions using time series. Some of these methods include:
- Moving average
- ARIMA
- Exponential smoothing
Deterministic Systems
A deterministic system always produces the same results for a given state or condition. In a deterministic system, variation and randomness do not influence how inputs are converted to outputs. A non-deterministic system works in contrast to a deterministic system. A non-deterministic model involves choice and randomness. Deterministic programming is like a traditional linear regression where x will always have the same value and leads to action Y. In a non-deterministic system, the input x often leads to multiple actions.
Non-linear differential equations
Non-linear differential equation problems are diverse. The technique or analysis used to find a solution depends on the problem. Non-linear differential equations are widely used in other disciplines. For example, Navier-Stokes equations in fluid dynamics, Black-Scholes PDE in finance, and Lotka-Volterra equations in Biology. One of the challenges of working with non-linear problems is that it is impossible to create new solutions from known solutions. This is possible with linear problems, where we can use the superposition principle to construct common solutions from a family of linearly independent solutions.