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 3.19% per annum.
- FCX price at the close of May 16, 2024 was $52.04 and was higher than the top border of the primary price channel by $1.81 (3.61%).
- The secondary trend is increasing.
- The growth rate of the secondary trend is 341.85% per annum.
- FCX price at the close of May 16, 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 FCX 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: February 4, 2021
End date: March 27, 2024
a = 3.5005
b = 0.0001
s = 0.1295
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 3.19%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.1295) – 1
= 67.86%
February 4, 2021 calculations
Top border of price channel:
Exp(Y433)
= Exp(a + b × X433 + 2 × s)
= Exp(a + b × 629 + 2 × s)
= Exp(3.5005 + 0.0001 × 629 + 2 × 0.1295)
= Exp(3.8136)
= $45.32
Bottom border of price channel:
Exp(Y433)
= Exp(a + b × X433 – 2 × s)
= Exp(a + b × 629 – 2 × s)
= Exp(3.5005 + 0.0001 × 629 – 2 × 0.1295)
= Exp(3.2957)
= $27.00
March 27, 2024 calculations
Top border of price channel:
Exp(Y1,223)
= Exp(a + b × X1,223 + 2 × s)
= Exp(a + b × 1,776 + 2 × s)
= Exp(3.5005 + 0.0001 × 1,776 + 2 × 0.1295)
= Exp(3.9123)
= $50.01
Bottom border of price channel:
Exp(Y1,223)
= Exp(a + b × X1,223 – 2 × s)
= Exp(a + b × 1,776 – 2 × s)
= Exp(3.5005 + 0.0001 × 1,776 – 2 × 0.1295)
= Exp(3.3943)
= $29.79
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 3.19% per annum.
- FCX price at the close of May 16, 2024 was $52.04 and was higher than the top border of the primary price channel by $1.81 (3.61%).
Secondary Trend
Start date: February 8, 2024
End date: May 16, 2024
a = -3.4320
b = 0.0041
s = 0.0425
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0041) – 1
= 341.85%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0425) – 1
= 18.54%
February 8, 2024 calculations
Top border of price channel:
Exp(Y1,190)
= Exp(a + b × X1,190 + 2 × s)
= Exp(a + b × 1,728 + 2 × s)
= Exp(-3.4320 + 0.0041 × 1,728 + 2 × 0.0425)
= Exp(3.6873)
= $39.94
Bottom border of price channel:
Exp(Y1,190)
= Exp(a + b × X1,190 – 2 × s)
= Exp(a + b × 1,728 – 2 × s)
= Exp(-3.4320 + 0.0041 × 1,728 – 2 × 0.0425)
= Exp(3.5172)
= $33.69
May 16, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(-3.4320 + 0.0041 × 1,826 + 2 × 0.0425)
= Exp(4.0862)
= $59.51
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(-3.4320 + 0.0041 × 1,826 – 2 × 0.0425)
= Exp(3.9161)
= $50.20
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 341.85% per annum.
- FCX price at the close of May 16, 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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