What are the different types of trading algorithms?

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ETF Arbitrage - concomitant on the task of ETF Market Making, there are many firms whose main aim is to outdo the ETF MMs with faster identification of arbitrage, and being in position to quickly close any open opportunities. They serve a useful purpose of both providing liquidity to the ETF in general, as well as help ETF MMs to close spreads faster. 

Event Arbitrage - certain market or news events create predictable volatility in the market which can be captured for short term gains. This may be caused by an impending company results or macro-economic release, or central bank actions. 

Statistical Arbitrage - many counters take their values from mathematical relationships with other measurable quantities or counters. For example, by their definition, Futures have a mean-reverting relationship with the underlying equities, while Options are related to their underlying via the Black Scholes equation, and Options are related to each other and the underlying equity via the Put Call Parity equation. While not traded in India, statistical arbitrage is used globally to take advantage of Interest Rate Parity relations.  

Latency Arbitrage - many firms have devoted themselves exclusively to optimizing their exchange connectivity, going to amazing lengths to upgrade from "low latency" and enter into "ultra-low latency" setups where they can simply stay ahead of other HFTs. This may include using microwave and fibre optic equipment. 

Automation - many system traders are able to formalize their thought process to an extent that they can lay out their strategy in programmable steps. Sometimes with the help of a professional programmer, and sometimes through self-taught programming, they are able to fully automate their strategies. The currently popular Intraday Short Strangle/Straddle is an example, also known as the "9:20 Strategy". 

Pattern Recognition - based on shapes traced by the price chart line, or OHLC patterns, it is one of the earliest styles of manual trading. At first it was simply a sub-type of Automated Algorithms, but with the advent of pattern recognition algorithms and AI/ML which can find patterns on its own, creating a niche on its own. It is the personal opinion of this writer that Rentec's first success was with an OHLC pattern recognition algorithm based on State Space analysis, specifically the Hidden Markov Model. 

Technical - perhaps the most popular style of algos, these are based on technical indicators, either individually, or in some linear combination. These are straightforward to conceive, prototype, test, and deploy. Most open source backtesting packages have builtin technical indicator libraries, making this style even more tractable. 

Predictive/Forecasting - while technical indicators run on recent historical data, predictive algorithms attempt to forecast the future, and take positions ahead of time. With AI/ML libraries becoming ubiquitous, and easy to use, predictive algorithms are beginning to become more popular. Especially attracted to these are students, data scientists, and other such highly technical professionals who use the underlying mathematics in their daily work. All that's left to do, at that point, is to port a model, which may be predicting shopping preferences (for example), and tune it to predict stock prices or volatility or any other market indicator. 

Sentiment - Natural Language Processing has been developing by leaps and bounds since 1960s, and with the advent of, first, "Big Data", and then AI/ML, it became possible for traders to reliably process large amount of text. A number of data sources are now available which stream various kinds of sentiment indicators, from social media blabber to earnings calls and US Fed announcements. While earnings calls and macro news is preferred for investments (see below) social market sentiment may be used for intraday trading on volatile days. 

Most investment strategies will revolve around creating a portfolio from initial conditions, and then recursively "re-balancing" it based on continuously monitoring of markets and data. In adverse events, monies are usually parked in risk-free assets, and not used for short positions or withdrawn completely from the market, unlike in case of trading. 

Factor Based - this approach starts with Nobel Prize winning Modern Portfolio Theory, which was initially a single factor based model that measured the portfolio level impact of constituents' risk (volatility calculated from standard deviation of returns) and the and returns (the arithmetic OR geometric average returns), and re-balanced a portfolio accordingly. Over time this theory was developed to include other fundamental factors such as the Capital Assets Pricing Model (CAPM) which factored in market capitalization and book-to-market ratio in addition to portfolio risk, for a total of 3 factors (hence also called 3-factor model). Of late, certain academics and practitioners have defined more than two dozen factors! 

Indicator Based - technical indicators are not the sole preserve of traders: investors who want a dynamic portfolio based more on market movements than company or economic fundamentals can always use, for example, a momentum indicator to re-balance their portfolios in real time, lowering the weight of a lower momentum stock and increasing that of a higher momentum stock. 

Sentiment - while a continuous stream of social sentiment regarding a stock is most useful to traders, longer term sentiment can be measured from scheduled calendar events like earnings declarations, earnings calls, analyst Q&A, and on a macro-economic scale from central bank statements and releases. This information is parsed in a slightly different manner than social sentiment because, say for example, a random market analyst from Bloomberg saying good things about a company in an analyst call will be interpreted differently from a CXO on an analyst Q&A saying good things about a company. 

Alternative Data - broadly, any data other than financial or economic data that is used for trading and investment is defined as "alternative data". That includes everything from news (minus financial and economic data), social media, weather data and so on. In fact, in a now-famous instance, UBS tied up with a  remote sensing company to forecast Walmart financials based on occupancy of its parking lots. In another instance, IHS Markit offers a running analysis of global trade (called GTAS) by measuring, among other things, the length of waiting queues at global ports.