Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is decreasing.
- The decline rate of the primary trend is 14.55% per annum.
- GILD price at the close of April 26, 2024 was $65.42 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 66.59% per annum.
- GILD price at the close of April 26, 2024 was inside the secondary price channel.
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of GILD price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: November 7, 2022
End date: October 12, 2023
a = 5.0162
b = -0.0004
s = 0.0254
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0004) – 1
= -14.55%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0254) – 1
= 10.70%
November 7, 2022 calculations
Top border of price channel:
Exp(Y890)
= Exp(a + b × X890 + 2 × s)
= Exp(a + b × 1,288 + 2 × s)
= Exp(5.0162 + -0.0004 × 1,288 + 2 × 0.0254)
= Exp(4.5122)
= $91.12
Bottom border of price channel:
Exp(Y890)
= Exp(a + b × X890 – 2 × s)
= Exp(a + b × 1,288 – 2 × s)
= Exp(5.0162 + -0.0004 × 1,288 – 2 × 0.0254)
= Exp(4.4105)
= $82.31
October 12, 2023 calculations
Top border of price channel:
Exp(Y1,123)
= Exp(a + b × X1,123 + 2 × s)
= Exp(a + b × 1,627 + 2 × s)
= Exp(5.0162 + -0.0004 × 1,627 + 2 × 0.0254)
= Exp(4.3661)
= $78.74
Bottom border of price channel:
Exp(Y1,123)
= Exp(a + b × X1,123 – 2 × s)
= Exp(a + b × 1,627 – 2 × s)
= Exp(5.0162 + -0.0004 × 1,627 – 2 × 0.0254)
= Exp(4.2644)
= $71.12
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 14.55% per annum.
- GILD price at the close of April 26, 2024 was $65.42 and was inside the primary price channel.
Secondary Trend
Start date: March 8, 2024
End date: April 26, 2024
a = 9.6649
b = -0.0030
s = 0.0111
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0030) – 1
= -66.59%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0111) – 1
= 4.54%
March 8, 2024 calculations
Top border of price channel:
Exp(Y1,224)
= Exp(a + b × X1,224 + 2 × s)
= Exp(a + b × 1,775 + 2 × s)
= Exp(9.6649 + -0.0030 × 1,775 + 2 × 0.0111)
= Exp(4.3552)
= $77.88
Bottom border of price channel:
Exp(Y1,224)
= Exp(a + b × X1,224 – 2 × s)
= Exp(a + b × 1,775 – 2 × s)
= Exp(9.6649 + -0.0030 × 1,775 – 2 × 0.0111)
= Exp(4.3108)
= $74.50
April 26, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(9.6649 + -0.0030 × 1,824 + 2 × 0.0111)
= Exp(4.2080)
= $67.22
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(9.6649 + -0.0030 × 1,824 – 2 × 0.0111)
= Exp(4.1637)
= $64.31
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 66.59% per annum.
- GILD price at the close of April 26, 2024 was inside the secondary price channel.
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
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