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## Transversality Condition

This condition is a necessary condition that determines the optimal path for dynamic models. A transversality equation is often used to complement the Euler equation. It allows you to identify the precise optimal path. This condition is vital because it eliminates explosive consumption. Transversality conditions also save paths that may end up in too much consumption that would drive the economy's capital path to zero.

## Ito’s lemma

Ito's lemma is used to compute the time-dependent stochastic process’ derivate. This component is vital in Ito Calculus. Also, it is intrinsic to the process of deriving the Black-Scholes equation for contingent options pricing. It is also the foundation of quantitative finance. To understand Ito's lemma, you must have background knowledge of stochastic differential equations, Brownian motion, and geometric Brownian motion. In a stochastic process, Ito's lemma can be used instead of the chain rule.

## Time-series analysis and forecasting

Time series analysis analyzes and extracts meaningful statistics from time-series data. On the other hand, time series forecasting involves the use of a model to predict future values from the values previously observed. Time series analysis and forecasting are extensively used for non-stationary data such as stock price, weather, retail sales, economic data, etc. Here are some of the methods that are used to model time series data and make predictions.

### 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 excellent at identifying exciting trends in data.

### Exponential smoothing

The exponential smoothing model follows the same notion 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