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 7.27% per annum.
- FCX price at the close of January 17, 2025 was $40.22 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 61.40% per annum.
- FCX price at the close of January 17, 2025 was higher than the top border of the secondary price channel by $0.41 (1.02%). This indicates a possible reversal in the secondary trend direction.
- The direction of the secondary trend is opposite to the direction of the primary trend. This indicates a possible reversal in the direction of the primary trend.
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: January 17, 2025
a = 3.4295
b = 0.0002
s = 0.1337
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0002) – 1
= 7.27%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.1337) – 1
= 70.70%
February 4, 2021 calculations
Top border of price channel:
Exp(Y263)
= Exp(a + b × X263 + 2 × s)
= Exp(a + b × 380 + 2 × s)
= Exp(3.4295 + 0.0002 × 380 + 2 × 0.1337)
= Exp(3.7699)
= $43.38
Bottom border of price channel:
Exp(Y263)
= Exp(a + b × X263 – 2 × s)
= Exp(a + b × 380 – 2 × s)
= Exp(3.4295 + 0.0002 × 380 – 2 × 0.1337)
= Exp(3.2352)
= $25.41
January 17, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(3.4295 + 0.0002 × 1,823 + 2 × 0.1337)
= Exp(4.0473)
= $57.24
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(3.4295 + 0.0002 × 1,823 – 2 × 0.1337)
= Exp(3.5125)
= $33.53
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 7.27% per annum.
- FCX price at the close of January 17, 2025 was $40.22 and was inside the primary price channel.
Secondary Trend
Start date: September 26, 2024
End date: January 17, 2025
a = 8.3842
b = -0.0026
s = 0.0270
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0026) – 1
= -61.40%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0270) – 1
= 11.39%
September 26, 2024 calculations
Top border of price channel:
Exp(Y1,179)
= Exp(a + b × X1,179 + 2 × s)
= Exp(a + b × 1,710 + 2 × s)
= Exp(8.3842 + -0.0026 × 1,710 + 2 × 0.0270)
= Exp(3.9789)
= $53.46
Bottom border of price channel:
Exp(Y1,179)
= Exp(a + b × X1,179 – 2 × s)
= Exp(a + b × 1,710 – 2 × s)
= Exp(8.3842 + -0.0026 × 1,710 – 2 × 0.0270)
= Exp(3.8710)
= $47.99
January 17, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(8.3842 + -0.0026 × 1,823 + 2 × 0.0270)
= Exp(3.6842)
= $39.81
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(8.3842 + -0.0026 × 1,823 – 2 × 0.0270)
= Exp(3.5763)
= $35.74
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 61.40% per annum.
- FCX price at the close of January 17, 2025 was higher than the top border of the secondary price channel by $0.41 (1.02%). 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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