Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 85.44% per annum.
- GILD price at the close of February 20, 2025 was $110.03 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 52.86% per annum.
- GILD price at the close of February 20, 2025 was higher than the top border of the secondary price channel by $4.34 (4.11%).
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: April 18, 2024
End date: February 20, 2025
a = 1.5455
b = 0.0017
s = 0.0383
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0017) – 1
= 85.44%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0383) – 1
= 16.58%
April 18, 2024 calculations
Top border of price channel:
Exp(Y1,046)
= Exp(a + b × X1,046 + 2 × s)
= Exp(a + b × 1,518 + 2 × s)
= Exp(1.5455 + 0.0017 × 1,518 + 2 × 0.0383)
= Exp(4.1906)
= $66.06
Bottom border of price channel:
Exp(Y1,046)
= Exp(a + b × X1,046 – 2 × s)
= Exp(a + b × 1,518 – 2 × s)
= Exp(1.5455 + 0.0017 × 1,518 – 2 × 0.0383)
= Exp(4.0372)
= $56.67
February 20, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(1.5455 + 0.0017 × 1,826 + 2 × 0.0383)
= Exp(4.7117)
= $111.24
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(1.5455 + 0.0017 × 1,826 – 2 × 0.0383)
= Exp(4.5583)
= $95.42
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 85.44% per annum.
- GILD price at the close of February 20, 2025 was $110.03 and was inside the primary price channel.
Secondary Trend
Start date: September 12, 2024
End date: February 20, 2025
a = 2.4770
b = 0.0012
s = 0.0302
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0012) – 1
= 52.86%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0302) – 1
= 12.84%
September 12, 2024 calculations
Top border of price channel:
Exp(Y1,147)
= Exp(a + b × X1,147 + 2 × s)
= Exp(a + b × 1,665 + 2 × s)
= Exp(2.4770 + 0.0012 × 1,665 + 2 × 0.0302)
= Exp(4.4733)
= $87.65
Bottom border of price channel:
Exp(Y1,147)
= Exp(a + b × X1,147 – 2 × s)
= Exp(a + b × 1,665 – 2 × s)
= Exp(2.4770 + 0.0012 × 1,665 – 2 × 0.0302)
= Exp(4.3525)
= $77.67
February 20, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(2.4770 + 0.0012 × 1,826 + 2 × 0.0302)
= Exp(4.6605)
= $105.69
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(2.4770 + 0.0012 × 1,826 – 2 × 0.0302)
= Exp(4.5397)
= $93.66
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 52.86% per annum.
- GILD price at the close of February 20, 2025 was higher than the top border of the secondary price channel by $4.34 (4.11%).
- 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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