From ead6d8d90fcd808f5da1150b87fe7a2e4eac8990 Mon Sep 17 00:00:00 2001 From: Micah Kendall Date: Thu, 5 Sep 2024 15:56:53 +1000 Subject: [PATCH] gema rename --- .github/workflows/build.yml | 2 +- build.sh | 2 +- ema.typ | 95 --------------------------------- gema.typ | 101 ++++++++++++++++++++++++++++++++++++ img/example.png | Bin 82258 -> 75537 bytes oracles.py | 29 ++++------- 6 files changed, 112 insertions(+), 117 deletions(-) delete mode 100644 ema.typ create mode 100644 gema.typ diff --git a/.github/workflows/build.yml b/.github/workflows/build.yml index dc07494..f235a2e 100644 --- a/.github/workflows/build.yml +++ b/.github/workflows/build.yml @@ -53,7 +53,7 @@ jobs: tag_name: ${{ github.ref_name }} files: "./*.pdf" - - run: "mkdir output && mv ema.pdf output/ema.pdf" + - run: "mkdir output && mv gema.pdf output/gema.pdf" - name: Publish uses: ryand56/r2-upload-action@latest diff --git a/build.sh b/build.sh index 5d70c56..769a0a0 100755 --- a/build.sh +++ b/build.sh @@ -1 +1 @@ -typst c ema.typ \ No newline at end of file +typst c gema.typ \ No newline at end of file diff --git a/ema.typ b/ema.typ deleted file mode 100644 index cb835a3..0000000 --- a/ema.typ +++ /dev/null @@ -1,95 +0,0 @@ -#let special_version = read("./version.txt") -#align(center, [ - #v(2em) - #[#set par(justify: true) - #image("img/logo-black.png", width: 120pt)] - #set text(size:18pt) - - Oracle Specifications - #align(center, text(12pt, weight: 400)[ - v. #special_version - ]) - - #datetime.today().display("[day] [month repr:long], [year]") -]) -#v(2em) -= Simple EMA Oracle Specification - -== Overview -This specification outlines the Simple Exponential Moving Average (EMA) oracle algorithm, which is designed to provide a responsive and adaptive measure of asset price trends. The algorithm is particularly suited for financial applications where quick reactions to market downturns are crucial while maintaining stability during upward trends. - -== Algorithm Description -The Simple EMA algorithm uses a single piece of previous state to add a drag for any price increases while immediately reflecting price decreases. This approach combines the benefits of quick responsiveness to potential losses with the stability of trend following during growth periods. - -== Key Features -1. Immediate reflection of price decreases -2. Smoothed response to price increases using EMA calculation -3. Single state variable for efficient implementation - -== Implementation Details - -=== Inputs -- `prices`: A list of asset prices over time -- `period`: The number of days for the EMA calculation (default: 20) - -=== Output -- A list of EMA values corresponding to the input prices - -== Visual Representation - -The following graph illustrates the behavior of the Simple EMA algorithm compared to the actual price of an asset over time: - -#figure( - image("img/example.png", width: 80%), - caption: [ - Comparison of Asset Price and Simple EMA over time. - The red line represents the Simple EMA, which quickly adapts to price decreases while smoothing price increases. - ] -) - -This visual representation demonstrates how the Simple EMA (red line) closely follows the asset price (blue line) during downward movements, while providing a smoother trend during upward movements. This behavior aligns with the algorithm's design to be responsive to potential losses while maintaining stability during growth periods. - - -=== Pseudocode -#figure( - align(left)[ - #set text(font: "New Computer Modern Mono") - #set par(leading: 0.65em) - #let prices = [...price values] - - #table( - columns: (auto, auto), - inset: 0pt, - stroke: none, - align: left + horizon, - [*Input:*], [prices, period], - [*Output:*], [ema], - ) - - #v(0.5em) - $"ema" arrow.l [prices[0]]$\ - $"multiplier" arrow.l 2 / ("period" + 1)$\ - #v(0.5em) - *for* $"price"$ *in* $"prices"[1:]$ *do*\ - #h(1em) *if* $"price" < "ema"[-1]$ *then*\ - #h(2em) $"ema"."append"("price")$\ - #h(1em) *else*\ - #h(2em) $"new_ema" arrow.l ("price" - "ema"[-1]) dot "multiplier" + "ema"[-1]$\ - #h(2em) $"ema"."append"("new_ema")$\ - #h(1em) *end if*\ - *end for* - #v(0.5em) - *return* $"ema"$ - ], - caption: "Simple EMA Algorithm" -) - -== Notes -1. The algorithm initializes the EMA with the first price in the series. -2. For each subsequent price: - - If the new price is lower than the previous EMA, it immediately becomes the new EMA value. - - If the new price is higher, a standard EMA calculation is applied. -3. This approach ensures quick adaptation to price drops while smoothing out price increases. - -== Reference Implementation -For a reference implementation, refer to the `calculate_simple_ema` function in the `oracles.py` file. diff --git a/gema.typ b/gema.typ new file mode 100644 index 0000000..533d8cc --- /dev/null +++ b/gema.typ @@ -0,0 +1,101 @@ +#let special_version = read("./version.txt") +#align(center, [ + #v(2em) + #[#set par(justify: true) + #image("img/logo-black.png", width: 120pt)] + #set text(size:18pt) + + Oracle Specifications + #align(center, text(12pt, weight: 400)[ + v. #special_version + ]) + + #datetime.today().display("[day] [month repr:long], [year]") +]) +#v(2em) += GEMA Oracle Specification + +== Overview +This specification outlines the Greater Exponential Moving Average (GEMA) oracle algorithm, designed to provide a responsive and adaptive measure of asset price trends. It is particularly suited for financial applications requiring quick reactions to market downturns while maintaining stability during upward trends. + +== Algorithm Description +The GEMA algorithm uses a single piece of previous state to add a drag for price increases while immediately reflecting decreases. This approach combines quick responsiveness to potential losses with the stability of trend following during growth periods. + +== Key Features +1. Immediate reflection of price decreases +2. Smoothed response to price increases using GEMA calculation +3. Single state variable for efficient implementation + +== Implementation Details + +=== Inputs +- `prices`: A list of asset prices over time +- `period`: The number of days for the GEMA calculation (default: 20) + +=== Output +- A list of GEMA values corresponding to the input prices + +== Visual Representation + +#figure( + image("img/example.png", width: 80%), + caption: [ + Comparison of Asset Price and GEMA over time. + The red line represents the GEMA, which quickly adapts to price decreases while smoothing price increases. + ] +) + +This graph demonstrates how the GEMA (red line) closely follows the asset price (blue line) during downward movements, while providing a smoother trend during upward movements. + +=== Algorithm +#figure( +$f(t) = min { + gamma dot f(t-1) + (1-gamma) x_t, + x_t +}$, +caption: "GEMA Algorithm" +) + +=== Pseudocode +#figure( + align(left)[ + #set text(font: "New Computer Modern Mono") + #set par(leading: 0.65em) + #let prices = [...price values] + + #table( + columns: (auto, auto), + inset: 0pt, + stroke: none, + align: left + horizon, + [*Input:*], [prices, period], + [*Output:*], [gema], + ) + + #v(0.5em) + $"gema" arrow.l [prices[0]]$\ + $"multiplier" arrow.l 2 / ("period" + 1)$\ + #v(0.5em) + *for* $"price"$ *in* $"prices"[1:]$ *do*\ + #h(1em) *if* $"price" < "gema"[-1]$ *then*\ + #h(2em) $"gema"."append"("price")$\ + #h(1em) *else*\ + #h(2em) $"new_gema" arrow.l ("price" - "gema"[-1]) dot "multiplier" + "gema"[-1]$\ + #h(2em) $"gema"."append"("new_gema")$\ + #h(1em) *end if*\ + *end for* + #v(0.5em) + *return* $"gema"$ + ], + caption: "GEMA Algorithm" +) + +== Notes +1. The algorithm initializes the GEMA with the first price in the series. +2. For each subsequent price: + - If the new price is lower than the previous GEMA, it immediately becomes the new GEMA value. + - If the new price is higher, a standard GEMA calculation is applied. +3. This approach ensures quick adaptation to price drops while smoothing out price increases. + +== Reference Implementation +For a reference implementation, refer to the `calculate_gema` function in the `oracles.py` file. diff --git a/img/example.png b/img/example.png index 1955704f2f04de95595df4ecf22a469f71f44653..51d9dc2ce923b1eaa5d9cf7c4051d8f96b4f6ec2 100644 GIT binary patch literal 75537 zcmeFZbySpH^fo+*f|4RimkJ^xAzj0OD2kMTbW2GMF?1_RNC_yNih!hmFm!iIcXxLU z@ts?Je((FO_5Jnz_pbG_77vdwb93%<_P+LYU3=g7zm$7Mh)0D7gTV-;oDrmV7eTwHYIaIi#&(YSwni{neLHIlD?1C**9;CuwkT68BsaStJJ&;o zH+FW`C?O6G%l~-+yOpg8$89<6VQ`Ua*3Z>ZFc`5u^of;@NHc|D!C+EP#9ukZt&KZ6 zY0eKfZRbWXZN>|9PT*hC@A_HyhVnxM?Q``H`7AH*TP9oF|0bqx_4fU6{vn?0hg(;# zefm@pd01o-w0mx2XV?;9IUJ$7gV7?7G>YGE4)fkbO?I6P5!7*BC;9Ucs$;adj^+37 zEG9$ zz^*L)ed!%{um5#fvHyG7P|^QWHevbDxHGQBkL0e4D@C?Okp*RMnmjW%H)(7~BWrGX z&!|M$RleAu)ts^%wD0XZcfLY#;xf24T#z?xF?}IIM?BjYH2V&pU9T;ItpZ;DUf^u6 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-10,20 +10,9 @@ def generate_price_data(initial_price, num_days, volatility): prices.append(new_price) return prices -def calculate_modified_ema(prices, period=20): - """Calculate Modified Exponential Moving Average.""" - ema = [prices[0]] - multiplier = 2 / (period + 1) - for price in prices[1:]: - if price < ema[-1]: - ema.append(price) # Immediately adjust to price decrease - else: - ema.append((price - ema[-1]) * multiplier + ema[-1]) # Use EMA for price increase - return ema - -def calculate_simple_ema(prices, period=20): +def calculate_gema(prices, period=20): """ - Calculate Simple Exponential Moving Average with immediate price decrease reflection. + Calculate Greater Exponential Moving Average with immediate price decrease reflection. This is the preferred model for our analysis. It has the following characteristics: 1. Immediately adjusts to price decreases, providing quick responsiveness to market downturns. @@ -31,24 +20,24 @@ def calculate_simple_ema(prices, period=20): This combination allows for quick reaction to potential losses while maintaining trend stability during growth periods. """ - ema = [prices[0]] + gema = [prices[0]] multiplier = 2 / (period + 1) for price in prices[1:]: - if price < ema[-1]: - ema.append(price) # Immediately adjust to price decrease + if price < gema[-1]: + gema.append(price) # Immediately adjust to price decrease else: - ema.append((price - ema[-1]) * multiplier + ema[-1]) # Use EMA for price increase - return ema + gema.append((price - gema[-1]) * multiplier + gema[-1]) # Use EMA for price increase + return gema def plot_asset_price(asset_name, initial_price=100, num_days=365, volatility=1): """Plot the price of an asset over time.""" days = range(num_days) prices = generate_price_data(initial_price, num_days, volatility) - simple_ema = calculate_simple_ema(prices) + gema = calculate_gema(prices) plt.figure(figsize=(10, 6)) plt.plot(days, prices, label='Price') - plt.plot(days, simple_ema, label='Simple EMA (Preferred Model)', color='red') + plt.plot(days, gema, label='GEMA (Preferred Model)', color='red') plt.title(f"Price of {asset_name} Over Time") plt.xlabel("Days") plt.ylabel("Price")