DocumentationCitations adopted ✨

docs/make.jl

@@ -13,7 +13,8 @@ makedocs(;
     plugins=[bib],
     format=Documenter.HTML(;
         canonical="https://shayandavoodii.github.io/OnlinePortfolioSelection.jl",
-        prettyurls = get(ENV, "CI", nothing) == "true"
+        prettyurls = get(ENV, "CI", nothing) == "true",
+        assets=String["assets/citations.css"],
     ),
     pages=Any[
         "Home" => "index.md",

docs/src/Combined.md

@@ -5,7 +5,7 @@ Nowadays researchers are trying to take advantage of each strategy and propose n
 2. MRvol
 
 ## LOcal ADaptive learning system (LOAD)
-[Guan & An (2019)](https://doi.org/10.1016/j.knosys.2019.104958) proposed a new OPS method, named LOcal ADaptive learning system (LOAD), which is a combination of the Follow the Winner (FW) and Follow the Loser principles. They tried to find the stocks that have a positive trend in the most recent time window by fitting a linear regression on the price data of the stocks against time. They used momentum principle to predict the next price of assets in this case. On the other hand, for the stocks that does not have a satisfactory trend in the most recent time window, they used the mean reversion principle to predict the next price of assets. They claim that through this fusion, the overall system can be more adaptive and effective than systems based on single strategies. After predicting the next prices, the next relative prices are predicted and used in the portfolio optimization.
+[GUAN2019104958](@citet) proposed a new OPS method, named LOcal ADaptive learning system (LOAD), which is a combination of the Follow the Winner (FW) and Follow the Loser principles. They tried to find the stocks that have a positive trend in the most recent time window by fitting a linear regression on the price data of the stocks against time. They used momentum principle to predict the next price of assets in this case. On the other hand, for the stocks that does not have a satisfactory trend in the most recent time window, they used the mean reversion principle to predict the next price of assets. They claim that through this fusion, the overall system can be more adaptive and effective than systems based on single strategies. After predicting the next prices, the next relative prices are predicted and used in the portfolio optimization.
 
 ### Run LOAD
 
@@ -64,7 +64,7 @@ It is worht mentioning that each metric can be accessed individually by writing
 
 ## MRvol
 
-Combination of meta-learning algorithms with other strategies are also investogated. For example, [Lin et al. (2023)](https://doi.org/10.1016/j.eswa.2023.121472) proposed a new OPS method, named MRvol, which is a combination of the Follow the Loser (FL) and Meta-Learning (ML) strategies. First, they try to select the stocks that have the relative price bellow than 1 as the first filter, and then search for the stock that have the most relative volume value among the filtered stocks as the second filter. Then, they apply a meta-algorithm to integrate expert opinions (i.e., expert strategies), which are obtained based on mean reversion and trading volume. Thirdly, they determine the window size of the expert strategy as W and establish an expert strategy. When the expert constructs a stock portfolio, he/she identifies an investment target asset for each period, so there are W investment target assets. As they said, in order to reduce investment risk and increase diversification of investment, this paper considers using moving window data of different sizes to construct a pool of expert strategies, which is also called a pool of expert opinions, and then applies meta-algorithm in machine learning technique to integrate expert opinions to propose an investment strategy.
+Combination of meta-learning algorithms with other strategies are also investogated. For example, [LIN2024121472](@citet) proposed a new OPS method, named MRvol, which is a combination of the Follow the Loser (FL) and Meta-Learning (ML) strategies. First, they try to select the stocks that have the relative price bellow than 1 as the first filter, and then search for the stock that have the most relative volume value among the filtered stocks as the second filter. Then, they apply a meta-algorithm to integrate expert opinions (i.e., expert strategies), which are obtained based on mean reversion and trading volume. Thirdly, they determine the window size of the expert strategy as W and establish an expert strategy. When the expert constructs a stock portfolio, he/she identifies an investment target asset for each period, so there are W investment target assets. As they said, in order to reduce investment risk and increase diversification of investment, this paper considers using moving window data of different sizes to construct a pool of expert strategies, which is also called a pool of expert opinions, and then applies meta-algorithm in machine learning technique to integrate expert opinions to propose an investment strategy.
 
 ### Run MRvol
 

docs/src/FL.md

@@ -9,7 +9,7 @@ The "Follow the Loser" (FL) strategy, introduced by Borodin and [Vincent (2004)]
 
 ## Reweighted Price Relative Tracking System for Automatic Portfolio Optimization (RPRT)
 
-RPRT, a "Follow the Loser" (FL) strategy introduced by [Lai et al. (2018)](https://doi.org/10.1109/TSMC.2018.2852651), automatically allocates distinct weights to price relative predictions based on each asset's performance during the price prediction phase. These weights are continually adjusted. In the portfolio optimization phase, the authors introduced a novel tracking system with a flexible increasing factor to maximize future wealth in the next period. Their study resulted in the design of an efficient algorithm to address portfolio optimization objectives, suitable for large-scale and time-limited scenarios. Through extensive experiments involving six benchmark datasets from real financial markets, encompassing varied assets and time spans, RPRT demonstrated superior performance compared to other state-of-the-art systems. It showcased better cumulative wealth, mean excess return, annual percentage yield, and typical risk metrics. Additionally, RPRT exhibited resilience to substantial transaction costs and delivered swift performance, highlighting its effectiveness and efficiency as an online portfolio selection system.
+RPRT, a "Follow the Loser" (FL) strategy introduced by [8411138](@citet), automatically allocates distinct weights to price relative predictions based on each asset's performance during the price prediction phase. These weights are continually adjusted. In the portfolio optimization phase, the authors introduced a novel tracking system with a flexible increasing factor to maximize future wealth in the next period. Their study resulted in the design of an efficient algorithm to address portfolio optimization objectives, suitable for large-scale and time-limited scenarios. Through extensive experiments involving six benchmark datasets from real financial markets, encompassing varied assets and time spans, RPRT demonstrated superior performance compared to other state-of-the-art systems. It showcased better cumulative wealth, mean excess return, annual percentage yield, and typical risk metrics. Additionally, RPRT exhibited resilience to substantial transaction costs and delivered swift performance, highlighting its effectiveness and efficiency as an online portfolio selection system.
 
 See [`rprt`](@ref).
 
@@ -83,7 +83,7 @@ It is worht mentioning that each metric can be accessed individually by writing
 
 ## Anti-Correlation (Anticor)
 
-Anticor is an FL strategy introduced by [Borodin and El-Yaniv (2004)](https://www.doi.org/10.1613/jair.1336). The strategy aims to capitalize on the mean-reversion attribute of asset prices. It transfers wealth from asset $i$ to asset $j$ within two consecutive market windows of size $w$ if the growth rate of asset $i$ exceeds that of asset $j$ in the most recent window. It is also contingent on a positive correlation between asset $i$ in the second last window and asset $j$ in the last window. The extent of wealth transferred from asset $i$ to $j$ depends on the correlation strength between the assets and the degree of "self-anti-correlations" for each asset $i$. [[1](https://rdrr.io/github/ngloe/olpsR/man/alg_Anticor.html)]
+Anticor is an FL strategy introduced by [borodin2003can](@citet). The strategy aims to capitalize on the mean-reversion attribute of asset prices. It transfers wealth from asset $i$ to asset $j$ within two consecutive market windows of size $w$ if the growth rate of asset $i$ exceeds that of asset $j$ in the most recent window. It is also contingent on a positive correlation between asset $i$ in the second last window and asset $j$ in the last window. The extent of wealth transferred from asset $i$ to $j$ depends on the correlation strength between the assets and the degree of "self-anti-correlations" for each asset $i$. [[1](https://rdrr.io/github/ngloe/olpsR/man/alg_Anticor.html)]
 
 See [`anticor`](@ref).
 
@@ -159,7 +159,7 @@ It is worht mentioning that each metric can be accessed individually by writing
 
 ## Online Moving Average Reversion (OLMAR)
 
-The OLMAR algorithm, short for On-Line Moving Average Reversion, introduces a novel approach to online portfolio selection. It incorporates multi-period mean reversion by utilizing “Moving Average Reversion” (MAR), which predicts next price relatives through moving averages. As far as the available literature indicates, OLMAR is the initial algorithm to employ moving averages within the framework of online portfolio selection [[1](https://www.sciencedirect.com/science/article/pii/S0004370215000168)]. While relatively straightforward, OLMAR includes a reasonable updating strategy and has been empirically validated through extensive real-market experiments.
+The OLMAR algorithm, short for On-Line Moving Average Reversion ([li2012online](@citet)), introduces a novel approach to online portfolio selection. It incorporates multi-period mean reversion by utilizing “Moving Average Reversion” (MAR), which predicts next price relatives through moving averages. As far as the available literature indicates, OLMAR is the initial algorithm to employ moving averages within the framework of online portfolio selection [LI2015104](@cite). While relatively straightforward, OLMAR includes a reasonable updating strategy and has been empirically validated through extensive real-market experiments.
 
 See [`olmar`](@ref).
 
@@ -233,7 +233,7 @@ It is worht mentioning that each metric can be accessed individually by writing
 
 ## Passive Aggressive Mean Reversion (PAMR)
 
-The Passive Aggressive Mean Reversion (PAMR) algorithm ([Li et al., 2012](https://www.doi.org/10.1007/s10994-012-5281-z)) is a machine learning model employed in the domain of quantitative finance, specifically designed for trading strategies in mean-reverting markets. PAMR employs a passive-aggressive learning approach to adjust portfolio weights in response to deviations from the mean, aiming to capitalize on mean reversion phenomena prevalent in financial markets. The algorithm's core component, the step size $\tau_t$, is determined by the ratio of the observed error $\ell_{\in}^t$ to the squared norm of the discrepancy between the current feature vector $\mathbf{x}_t$ and the mean feature vector $\bar{x}_t$ up to time $t$. The formula for the step size in PAMR is expressed as:
+The Passive Aggressive Mean Reversion (PAMR) algorithm ([Li2012-ks](@citet)) is a machine learning model employed in the domain of quantitative finance, specifically designed for trading strategies in mean-reverting markets. PAMR employs a passive-aggressive learning approach to adjust portfolio weights in response to deviations from the mean, aiming to capitalize on mean reversion phenomena prevalent in financial markets. The algorithm's core component, the step size $\tau_t$, is determined by the ratio of the observed error $\ell_{\in}^t$ to the squared norm of the discrepancy between the current feature vector $\mathbf{x}_t$ and the mean feature vector $\bar{x}_t$ up to time $t$. The formula for the step size in PAMR is expressed as:
 
 ```math
 \tau_t = \frac{{\ell_{\in}^t}}{{\left\| {\mathbf{x}_t - \bar{x}_t \mathbf{1}} \right\|^2}}
@@ -343,4 +343,7 @@ Annualized Standard Deviation: 0.2365856617445457
 
 In this case, the algorithm has a better performance in terms of the cumulative return, annualized sharpe ratio, and calmar ratio. However, the maximum drawdown is slightly higher than the PAMR algorithm. The same procedure can be applied to the PAMR-2 algorithm (see [`PAMR2`](@ref)).
 
-It is worht mentioning that each metric can be accessed individually by writing `results.` and pressing the `Tab` key. Note that one can individually investigate the performance of the algorithm regarding each metric. See [`sn`](@ref), [`ann_std`](@ref), [`apy`](@ref), [`ann_sharpe`](@ref), [`mdd`](@ref), and [`calmar`](@ref). See [Performance evaluation](@ref) section for more information.
+It is worht mentioning that each metric can be accessed individually by writing `results.` and pressing the `Tab` key. Note that one can individually investigate the performance of the algorithm regarding each metric. See [`sn`](@ref), [`ann_std`](@ref), [`apy`](@ref), [`ann_sharpe`](@ref), [`mdd`](@ref), and [`calmar`](@ref). See [Performance evaluation](@ref) section for more information.
+
+```@bibliography
+```

docs/src/FW.md

@@ -8,7 +8,7 @@ The Follow the Winner (FW) strategies operate on the principle that assets that
 
 ## Universal Portfolio
 
-Universal Portfolio (UP) is a Follow the Winner (FW) strategy introduced by [Cover (1991)](https://doi.org/10.1111/j.1467-9965.1991.tb00002.x). This algorithm is designed to optimize the cumulative return of a portfolio over the investment horizon. UP's approach is centered on daily stock market performance and the distribution of wealth invested in individual stocks.
+Universal Portfolio (UP) is a Follow the Winner (FW) strategy introduced by [COVER](@citet). This algorithm is designed to optimize the cumulative return of a portfolio over the investment horizon. UP's approach is centered on daily stock market performance and the distribution of wealth invested in individual stocks.
 
 See [`up`](@ref).
 
@@ -78,7 +78,7 @@ It is worht mentioning that each metric can be accessed individually by writing
 
 ## Exponential Gradient
 
-Exponential Gradient (EG) is a FW strategy introduced by [Helmbold et al. (1998)](https://onlinelibrary.wiley.com/doi/10.1111/1467-9965.00058). The authors assert that EG can nearly attain the same wealth as the best constant rebalanced portfolio (BCRP), discerned retrospectively from the actual market outcomes. This algorithm is notably straightforward to implement.
+Exponential Gradient (EG) is a FW strategy introduced by [https://doi.org/10.1111/1467-9965.00058](@citet). The authors assert that EG can nearly attain the same wealth as the best constant rebalanced portfolio (BCRP), discerned retrospectively from the actual market outcomes. This algorithm is notably straightforward to implement.
 
 See [`eg`](@ref).
 
@@ -146,7 +146,7 @@ It is worht mentioning that each metric can be accessed individually by writing
 
 ## Price Peak Tracking (PPT)
 
-The Price Peak Tracking (PPT) algorithm ([Lai et al., 2017](https://doi.org/10.1109/TNNLS.2017.2705658)) is a novel linear learning system for online portfolio selection, based on the idea of tracking control. The algorithm uses a transform function that aggressively tracks the increasing power of different assets, and allocates more investment to the better performing ones. The PPT objective can be solved by a fast backpropagation algorithm, which is suitable for large-scale and time-limited applications, such as high-frequency trading. The algorithm has been shown to outperform other state-of-the-art systems in computational time, cumulative wealth, and risk-adjusted metrics (See [`ppt`](@ref)).
+The Price Peak Tracking (PPT) algorithm ([7942104](@citet)) is a novel linear learning system for online portfolio selection, based on the idea of tracking control. The algorithm uses a transform function that aggressively tracks the increasing power of different assets, and allocates more investment to the better performing ones. The PPT objective can be solved by a fast backpropagation algorithm, which is suitable for large-scale and time-limited applications, such as high-frequency trading. The algorithm has been shown to outperform other state-of-the-art systems in computational time, cumulative wealth, and risk-adjusted metrics (See [`ppt`](@ref)).
 
 Let's run the algorithm on the real market data.
 
@@ -202,4 +202,7 @@ julia> results.MER
 -0.15974968844419762
 ```
 
-It is worht mentioning that each metric can be accessed individually by writing `results.` and pressing the `Tab` key. Note that one can individually investigate the performance of the algorithm regarding each metric. See [`sn`](@ref), [`ann_std`](@ref), [`apy`](@ref), [`ann_sharpe`](@ref), [`mdd`](@ref), and [`calmar`](@ref). See [Performance evaluation](@ref) section for more information.
+It is worht mentioning that each metric can be accessed individually by writing `results.` and pressing the `Tab` key. Note that one can individually investigate the performance of the algorithm regarding each metric. See [`sn`](@ref), [`ann_std`](@ref), [`apy`](@ref), [`ann_sharpe`](@ref), [`mdd`](@ref), and [`calmar`](@ref). See [Performance evaluation](@ref) section for more information.
+
+```@bibliography
+```

docs/src/ML.md

@@ -6,7 +6,7 @@ Meta-learning strategies are employed to combine opinions from experts to formul
 
 ## Combination Weights based on Online Gradient Descent (CW-OGD)
 
-[Zhang et al. (2021)](https://doi.org/10.1016/j.knosys.2021.107533) introduced a novel online portfolio selection algorithm leveraging a weighted learning technique and an online gradient descent algorithm. Their strategy demonstrates enhanced robustness by integrating various expert strategies and successfully addresses the challenge of complex computational time. To begin, the authors establish an expert pool encompassing numerous basic expert strategies, among which the strategy investing in a single stock is chosen as the fundamental expert strategy. Subsequently, they employ a loss function to assess the performance of each basic expert strategy and utilize the OGD algorithm to adjust the weight vector for the experts based on their losses.
+[ZHANG2021107533](@citet) introduced a novel online portfolio selection algorithm leveraging a weighted learning technique and an online gradient descent algorithm. Their strategy demonstrates enhanced robustness by integrating various expert strategies and successfully addresses the challenge of complex computational time. To begin, the authors establish an expert pool encompassing numerous basic expert strategies, among which the strategy investing in a single stock is chosen as the fundamental expert strategy. Subsequently, they employ a loss function to assess the performance of each basic expert strategy and utilize the OGD algorithm to adjust the weight vector for the experts based on their losses.
 
 ### Run CW-OGD
 
@@ -70,4 +70,5 @@ juila> metrics.Sn
 The result indicates that if we had invested in the given period, we would have gained ~3.2% profit.
 It is worht mentioning that each metric can be accessed individually by writing `results.` and pressing the `Tab` key. Note that one can individually investigate the performance of the algorithm regarding each metric. See [`sn`](@ref), [`ann_std`](@ref), [`apy`](@ref), [`ann_sharpe`](@ref), [`mdd`](@ref), and [`calmar`](@ref). See [Performance evaluation](@ref) section for more information.
 
-            
+```@bibliography
+```