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 3.14% per annum.
- FCX price at the close of May 2, 2024 was $48.78 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 579.33% per annum.
- FCX price at the close of May 2, 2024 was lower than the bottom border of the secondary price channel by $2.50 (4.87%). This indicates a possible reversal in the secondary trend direction.
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 5, 2021
End date: March 27, 2024
a = 3.5012
b = 0.0001
s = 0.1294
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 3.14%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.1294) – 1
= 67.79%
February 5, 2021 calculations
Top border of price channel:
Exp(Y444)
= Exp(a + b × X444 + 2 × s)
= Exp(a + b × 644 + 2 × s)
= Exp(3.5012 + 0.0001 × 644 + 2 × 0.1294)
= Exp(3.8145)
= $45.35
Bottom border of price channel:
Exp(Y444)
= Exp(a + b × X444 – 2 × s)
= Exp(a + b × 644 – 2 × s)
= Exp(3.5012 + 0.0001 × 644 – 2 × 0.1294)
= Exp(3.2970)
= $27.03
March 27, 2024 calculations
Top border of price channel:
Exp(Y1,233)
= Exp(a + b × X1,233 + 2 × s)
= Exp(a + b × 1,790 + 2 × s)
= Exp(3.5012 + 0.0001 × 1,790 + 2 × 0.1294)
= Exp(3.9116)
= $49.98
Bottom border of price channel:
Exp(Y1,233)
= Exp(a + b × X1,233 – 2 × s)
= Exp(a + b × 1,790 – 2 × s)
= Exp(3.5012 + 0.0001 × 1,790 – 2 × 0.1294)
= Exp(3.3940)
= $29.79
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 3.14% per annum.
- FCX price at the close of May 2, 2024 was $48.78 and was inside the primary price channel.
Secondary Trend
Start date: February 8, 2024
End date: April 19, 2024
a = -5.5744
b = 0.0052
s = 0.0366
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0052) – 1
= 579.33%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0366) – 1
= 15.78%
February 8, 2024 calculations
Top border of price channel:
Exp(Y1,200)
= Exp(a + b × X1,200 + 2 × s)
= Exp(a + b × 1,742 + 2 × s)
= Exp(-5.5744 + 0.0052 × 1,742 + 2 × 0.0366)
= Exp(3.6429)
= $38.20
Bottom border of price channel:
Exp(Y1,200)
= Exp(a + b × X1,200 – 2 × s)
= Exp(a + b × 1,742 – 2 × s)
= Exp(-5.5744 + 0.0052 × 1,742 – 2 × 0.0366)
= Exp(3.4964)
= $33.00
April 19, 2024 calculations
Top border of price channel:
Exp(Y1,249)
= Exp(a + b × X1,249 + 2 × s)
= Exp(a + b × 1,813 + 2 × s)
= Exp(-5.5744 + 0.0052 × 1,813 + 2 × 0.0366)
= Exp(4.0156)
= $55.46
Bottom border of price channel:
Exp(Y1,249)
= Exp(a + b × X1,249 – 2 × s)
= Exp(a + b × 1,813 – 2 × s)
= Exp(-5.5744 + 0.0052 × 1,813 – 2 × 0.0366)
= Exp(3.8691)
= $47.90
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 579.33% per annum.
- FCX price at the close of May 2, 2024 was lower than the bottom border of the secondary price channel by $2.50 (4.87%). This indicates a possible reversal in the secondary trend direction.
- 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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